Getting CS is about much more than just last hitting. In fact, solo laning itself revolves almost strictly around last hitting in high level play. You need to know how to balance all of the following:
Last Hitting: the skill of knowing how much damage you do to a minion to ensure that you obtain the gold from killing it.
Keeping the lane where you want it: This is a huge factor, some champions like Malzahar and Morganna can push harder than champions like Ryze because of their AoE abilities so should the Ryze player wish to keep the lane in the middle he must attack the wave more than just when the last hit is available.
Some champions however excel at killing minions under their own tower and may want to keep the lane there for safety while others have many escapes and can push to the enemy tower all they want and still escape back to their own should the enemy jungler gank. Part of mastering your favorite champions is learning how to balance risk vs reward with your available tool set.
Harassing: You also might not want to only keep an eye on the health bars of the enemy minions, you should also keep an eye on your own. This is especially important in top lane where the enemy usually last hits in melee range. Therefore you know where the enemy will need to be in order to get that gold. If you move or attack in such a way that they cannot reach that low hp minion without taking significant damage they will miss the gold or better. The #1 rule of hunting is: attack your prey when it attacks it's own.
Counters: Most champions have a wide array of other champions that they do particularly well against. Counters usually are formed when a champion excels in one of the above areas that their opponent lacks.
This is actually a huge topic that also tells a big part of the difference between a high and low elo player. It's also not that easy.
There is no real secret formula for when to push a lane or when to harras an opponent. You have to apply an own strategy for every matchup in the game. So I won't list every single possible matchup but I will give some examples.
First of all, even as support or jungler, knowing when to push or freeze a lane is a big factor of winning your lane. So now:
When should I push my lane?
Bot
- If you want to do dragon (Both sides)
- If you are Purple team and you are laning against someone who has problems with lasthitting under the turret
- If a pushed lane opens an opportunity to kill your opponent (if you have Blitzcrank/thresh for example and they can land a hook)
Mid
- If you want to do Dragon (Both sides)
- If you are laning against someone who has trouble lasthitting under the turret
- If you are laning against a roam dependent champion (Kassadin etc.)
Top
There are no real reasons to push top except for the ones that count for every lane.
Every lane
- If your jungler ganked successfully, push hard and try to get a turret
- If you want to get a lanegank going you will have to push. (except mid)
- Push as much lanes as possible if you are doing Nashor
- Push if your Lane opponent is missing so he loses farm under the turret
- If you want to towerdive
- And of course push if you can get a turret (2v1 lanes, or range vs meele)
When should I be freezing my lane?
Every lane
- If you want to harrass
- If you want to farm passively
- If you might get ganked but your jungler is near for a countergank
When should my lane get pushed by the opponent?
Every lane
- If you are expecting a gank
- If you have no trouble lasthitting under the turret
- If you are screwed easily by ganks
- If you want to make a longer escape path for the enemy (passive-aggressive playstyle)
- If you have a baaaad feeling about the position of the enemy jungler ;)
Now this counts for most situations, however there are some exceptions.
Example
You are playing Varus, Leona VS. Caitlyn, Janna.
Now if you go for what's above, you should get pushed since you can create a longer escape path for Janna who has no real escape spells and you also have no problems with farming under the turret as Varus. Also both of you have no escape spells so playing under the turret is safe right?
No! Caitlyn has a higher range than you and janna can disengage pretty easily. Also her shield will negate a huge part of the damage you deal to any of those two and she can push the turret even harder due to the bonus AD of the shield. In a matchup like this it would be better to just freeze the lane. You can still initiate if you have to but you won't lose a turret. Also if you position yourself right you won't get ganked that easily and in addition to that you can ward the bush to watch out for lane ganks.
When should I harras my Lane opponent?
Now this is also veeeery dependent on the matchup. In some cases it's easy: Whenever you can (Kayle VS. KhaZix for example). But most of the time it's a bit more complicated.
If you are range vs meele you generally want to harrass with autoattacks whenever you can and you want to punish your opponent hard if he goes in for a cs or tries to come to you.
If you are meele vs range you mostly want to focus on farming and rather go all in or trade heavily. Also if you are high range vs low Range (Caitlyn VS. Sivir for example) you also want to benefit from this with autoattack harrassment.
Now there isn't only meele vs range or high range vs low range. Unlike DotA, League heavily focuses on spells in lane. Now some champions have rather High costs while others have none at all. Here you have to know when to harass or trade with your spells since you can also harras an enemies mana pool if done right. If you are let's say Katarina VS. Sion you should always spam your Q so Sion has to either take the damage or use his shield which costs a lot of mana. But no matter what never lose Farm because of harrassment.
I hope this helps a bit but the topic is just too huge to be discussed online. I can really recommend the guides over at Solomid.net. They usually have good players writing in-depth guides which include the most common lane matchups and how to deal with them.
Best Answer
No, you cannot pick up the Eye of the Herald if your team wasn't the team that killed the Rift Herald. But denying it is still good as they will only get the 200 experience and 25 gold for killing it and not be able to push your turrets with it. If no one steps on it, it will remain on the ground for 40 seconds before disappearing.
source- personal experience and testing with the training tool.