What you need to know
The Siren doesn't play like other FPS games. The Siren makes full use of Borderlands' elemental effect system and requires a more tactical level of play. Sirens eschew guns that deal the most damage at once for guns that deal elemental effects.
When you start out as a Siren, the benefits aren't obvious. You don't get the elemental guns until you're a decent level (10+). You don't start getting the good elemental guns until a bit later.
You're going to deal less damage per shot compared to other classes. It's really hard to estimate how much damage your elemental effects deal too; don't focus on the numbers, focus on the chaos you wreak. You're going to kill a lot of people, even if it's not in one shot. And in Coop play you're especially valuable; your elemental effects will distract or weaken enemies for your group to finish off easily.
Also, I hope you enjoy the sound of people burning; you're going to hear a lot of it. It's the sound of progress, my friend.
Elements
You need to know elements. Read this, the whole thing. You need to eat, breath and excrete elemental effects.
Your 30% elemental effect chance means any elemental gun with a good rate of fire is a weapon of death in your hands, even if the same gun is near useless for other classes. Experienced players will know this and often offer up elemental guns to Sirens playing Coop. Lots of people don't like/don't understand/can't use elemental guns, so you can get first dibs. This means you won't get first dibs on the high damage, non-elemental guns...but you'll quickly find as a Siren, you don't really want those non-elemental guns anyway. I keep exactly zero non-elemental guns on standby.
Also, explosive isn't an element. Not for a Siren anyway; you get no bonus out of explosive guns, give them to someone else and pick up a gun that can melt some faces.
It's possible to play Siren without focusing on elemental damage...but it just doesn't make much sense. The elemental chance percent boost is insane and costs only 5 skill points for +30% chance per shot.
Patience
Good things come to those who wait. Things like the horrible burning demise of your enemies.
Since elemental guns do Damage Over Time you'll be able to leave an enemy for dead once they've taken enough damage and enough elemental effects have stacked on them for them to die without further gunfire. Take this time to reload more often, duck behind cover to recharge shields, or light up the next target.
As you play you'll get a feel for when an enemy is "done for"; this is the point when the passive elemental Damage Over Time is likely to kill the target with no more direct attacks from you. Watch health bars closely and you'll start to get a sense for this. Don't overkill targets; move on to the next enemy. Enemies with DOT effects shoot less anyway (they're panicked) so just leave them to die and start whittling down the next target.
Note that Shock, Fire and Corrosion all have different effect lengths and guns have different damage per second; you'll need to acquire this feel per gun but you'll be amazed how quickly you start to intuit when an enemy will die. The exact times are listed here, knowing the rough length of the stacked effects will help you estimate when you can stop shooting.
Phase Lock
Phaselock has two primary purposes; to disable a dangerous target for a time so you can focus on other enemies, or to disable a target so you can easily kill it.
Note Phase Lock holds the target still, usually with their Critical point exposed and stationary. This is a great opportunity for you or your teammates to pile on the damage.
Depending on skill tree you can turn Phase Lock into an elemental Area of Effect weapon, a tool for healing yourself/teammates or a way to control enemies (or some combination thereof). They all have their uses, generally I'd pick the Phase Lock variant based on the other skills in the related tree rather than picking the tree just for the Phase Lock skills; all of them work well. Experiment and respec to try all three as you gain enough skill points
Guns
Really the Siren can effectively use any kind of gun; the reload speed, magazine size, bullet velocity and damage boost skills help all guns pretty well. From Rocket Launchers to SMGs you'll be able to hit targets more easily and spend less time reloading. You don't have (explicitly) gun specific skills unlike other classes.
Your gun choice is mostly determined by elemental effects; since your +30% elemental effect chance is per bullet, fast guns make the most sense. In the time it takes to hit one target with an epic Rocket Launcher, you could have stacked insane Fire damage with an SMG of comparable stats and left the target for dead.
Note that most non-Siren players don't like/appreciate/use elemental guns. Many will immediately pass over any Maliwan weapon because, at a glance, they do less damage. You know that's not true, but you can use this to your advantage in coop; most players will willingly give first-dibs on elemental weapons to Sirens. Just ask and make sure it's cool with your friends; you get a lot more out of those guns than they can. If you're playing with other Sirens there may still be loot fights of course.
You will seriously need one gun for each elemental type. I actually keep one SMG and one Sniper Rifle for each elemental type, but try to have at least 3 different elements equipped at once and always be ready to switch to the right element for the job. You don't always need a Slag gun, but be sure to have Fire Shock and Corrosive at the ready.
Note however that your fast reload speed, increased magazine size and reduced damage per bullet (because elemental guns do less straight-up damage) means you're going to run out of bullets. A lot. You're going to want to make sure you have at least 3 or 4 different types of guns (even if you don't keep them all equipped).
Personally I keep around a supply of Sniper Rifles and SMGs with Pistols or Assault Rifles as backups. The SMGs and Snipers run out but I'm never completely out of ammo if I keep 3-4 gun types at once.
Summary
- Use Elemental guns. Only. Keep one of each element.
- Prefer Rapid Fire guns, but other types like Snipers are okay.
- Keep backup guns. You'll run out of ammo for your favorite gun.
- Be cold, calculated and clinical. Don't overkill, let your elemental damage finish off targets.
- Don't worry about doing less damage per hit. You'll know you're doing well because enemies die, not because you deal big numbers of damage at once.
- Use Phase Lock. At the least it keeps Badass enemies out of the fight for a few seconds, at best it's an invaluable tide turning weapon.
- Don't be afraid to play support; Sirens have skills that can be great offensive and defensive support to a whole coop team
Optimizing Zer0's talents for melee damage is somewhat trivial. Just greedily spend points on talents based on the amount of damage boost.
Killing Bl0w 5/5 (500% melee against low health)
Ir0n Hand 5/5 (15% melee)
Be Like Water 5/5 (30% melee)
Backstab 5/5 (40% melee from behind)
Execute (deception override)
Foll0wthr0ough 5/5 (40% melee after kill)
Many Must Fall (deception modifier)
C0unter Strike 5/5 250% counter damage
Ambush 5/5 (20% damage from behind)
Death Mark 1/1 (20% damage against targets previously hit by melee)
Rising sh0t (45% melee damage when fully stacked)
Headsh0t 2/5 (8% critical damage - would be 20% crit at 5/5)
Not taken : it was the smallest bonus and I'm out of points.
Like the Wind 5/5 (15% melee while moving)
I haven't actually played this, so... here's some advice or things to watch for if you try it:
If you find you can't stack Rising Sh0t, move those points to Headsh0t and Like the Wind.
If you find you can't get behind enemies (solo play might be tough to do this), move the points out of Ambush and Backstab.
If you find out that your melee damage is ok, but you need more Deception, or survivability... go for those talents that support that. Start by removing points from Ir0n hand (smallest bonus on the list).
If you find that you crit all the time, move points out of Ir0n hand into Headsh0t.
Best Answer
I pretty much only play solo, and I've got a level 72 zer0 and he is absolutely a blast. I've found that the most efficient way to play him for me was pure melee, especially for farming.
I've found two shield/gun combos to be effective and i'll go over them both.
The first is the law/order combo. You can get both of these for doing easy quests in sanctuary near the end of the main storyline. No killing of enemies required. The order is a shield that gives a pretty large boost with roid damage, and when you melee enemies with the law all damage you do to them also heals you.
The second is the rubi/love thumper combo. You get the rubi as a quest reward from moxxi for turning the "rakkaholics anonymous" quest in to her. the love thumper you'll get as a quest reward in overlook for doing the "best mothers day ever" quest. The best rubi to get is a slag rubi, if you have the time to spend farming the quest to get one. 12% of all damage you do with the rubi returns to you as health, and the love thumper is a pretty strong roid shield that also does explosive damage when depleted.
The reason you'll want either of these combos is because they heal you while you're in combat, and healing is one of the main things missing as a skill from Zer0's skill tree. This means you can get right up in the face of anything, and as long as you can hit them, you can generally let them wail on you without going down.
As for a build, i'd suggest going with this one.
and as you level up, try to work down the cunning tree to get death blossom (if you have the dlc's that let you level up past level 50). many must fall + death blossom in tandem is incredibly powerful.
the main strategy with this build is getting up in the face of what you are fighting, hit it to apply deathmark, let it take down your shield (so you get the roid damage buff and make counter-strike active), go into deception and get behind the enemy (hitting from behind activates ambush/backstab), wait until the deception timer is under 1 second left (to get the max melee damage boost from deception), and then smacking them with execute. it takes a good bit of practice, some set up, and some skill - but once you get the basic concept down... zer0 becomes VERY powerful. especially once you get the health of a major enemy down to ~30% when killing blow kicks in. if your enemy is slagged, you will be hitting them for MILLIONS each melee blow. one more point, is to try to go for critical hits as much as you can as they will basically double the damage you are doing.
if you have any more questions about anything specific - let me know. zer0 is probably one of the strongest solo players in the game, but he does require a little bit of equipment and practice to get that way