Spawning Location
When you first spawn you'll notice some text show up on the right side of the screen. This will contain your general location, so make sure you remember this. Unless you spawn near a landmark, it's the only way you'll have any idea where you spawned.
Map & Compass
There is an in-game map, but it's an item like any other. Until you find one and store it in your inventory it won't be displayed when you press M. However, there is an online version of the map, which also contains the English names of locations. Towns will have a sign containing their name somewhere near their borders, but it will be written in Cyrillic.
There is also an in-game compass, usable with K, but like the map is only usable if you have a compass in your inventory.
The map and the compass are the most important tools at your disposable for figuring out where you are, and what direction you need to walk in order to get where you want to go.
Night time
I haven't tried this method myself, but apparently there is a way to locate the North star at night. If you find yourself wandering around alone at night this should prove useful in helping you get around.
Finding Action
Towns are the best place to find zombies and players. Zombies have a much higher spawn rate in towns (in fact they currently don't spawn in the woods at all, only near buildings). Towns are also a required stop for most players since contain the most loot. Your best bet for finding a town after you spawn is to just follow the coast in either direction. It may take some time, but you'll eventually find a town.
Something else to pay attention to is the in-game chat (by default you talk with "/", and change channels with "."). Watching this is one of the best ways to find out where players and zombies are. Players will often send messages looking for people to meet-up with, or give out warnings if their are a lot of bandits or Zombies in an area.
Best Answer
The first thing you need to learn is which buildings contain loot - despite having lots of different building types, only a couple of buildings in DayZ are actually enterable, and even fewer of those regularly contain weapons.
Take a look at the DayZ DB Map, some good buildings to look in are
Check the DayZ Wiki or the DB for pictures / common locations of these buildings - recognising which buildings are likely contain loot that you want is very handy and shouldn't take long to learn (there are only a handful of "interesting" building types which contain loot)
When it comes to getting your first weapon there are a couple of different tactics - you can either take it slow, sticking to the outskirts and checking barns and other remote areas, or you can run into the middle of the biggest town you can find straight past all of the Zombies (and possibly players).
My preference is the second option - although unquestionably more risky, in the early stages you have very little to loose, and when it pays off you end up kitted out much much sooner than you would have been if you took it slowly. Initially I played it safe however had exactly the same experience as you - you have absolutely no weapons to start with (not even your fists), and sooner or later you are going to pick up a zombie no matter how careful you are. You might live longer, but you probably aren't any more likely to end up with a gun at the end of it.
Take a look at this video guide for a good root around my favourite city for looting my first weapon. The key to looting the big cities is to get in, get what you need and get out quickly. As soon as you have the basics that you need, get out - the longer you stay in a city, the more likely it is that you will loose your recently earned loot.