Where do I find supplies in DayZ?
Finding Supplies
Early on, there are two main types of locations you should rely on for supplies: Barns and the coastal cities.
Barns: Barns will normally only have a small number of zombies, and will normally contain a shotgun and some ammo. There are quite a few of them spread around the map, including near the coast where you spawn. Since they are located in the woods you are also less likely to run across other players, which can make them a lot safer than cities most of the time.
The problem with barns is that if there are a sizable amount of zombies around one it can be very hard if not impossible to get inside. Either way it's going to be a slow process. The key is to first observe the entire area, look for any openings, and slowly make your way through, only moving when you're certain it's safe to do so.
Deer stands: Deer stands are relatively safe and have a good chance of giving you a good primary weapon and/or ammo. And since they are often isolated and with their backs to forests, they can be looted quite securely, with only 2-3 zombies around.
Cities: The coastal cities (Chernogorsk, Elektrozavodsk, and Berezino) have a better chance of spawning supplies than Barns, but also contain more zombies, making it much more dangerous and difficult to navigate through. They also tend to be a hot spot for other players (especially bandits), so there's a greater chance of you getting attacked by other players. This also means there is more competition for supplies and you're more likely to just miss out on weapons which another player grabbed just shortly before you.
Avoid Getting Caught
There are a few things you should do (and avoid doing) in order to maximize your chances of survival, whether or not you have a weapon:
Stick to the Woods: Zombies (at least currently) don't spawn in the woods. They will only get there by following another player. Due to this you're very unlikely to come across zombies in the woods, making the woods a much safer option than traveling on the streets and through every random town you come across.
The woods also offers additional protection from other players, and for a few reasons. The first reason is that it's harder for players to see you due to all the trees and bushes. When players do find you it's also easier hide from them for the same reason. The size of the woods also makes it less likely for you'll come across other players, and also makes escape easier when you come across them. If you're running down the middle of the road then you're going to bump into everyone else running across that road.
Move Silently and Slowly: The quickest way to get caught, either by zombies or players, is sprinting through every city at full speed. When you're exploring a town or a city you need to move slowly, by moving while either crouched or prone. This makes you harder to see and harder to hear. Something else to take note of is that zombies have better vision than they do hearing, so crouch running is actually a fairly safe and efficient way to travel.
Be Aware of Your Surroundings: No matter how slowly you're moving, if you're not paying attention to what's around you you're going to die. Before crossing openings or entering building stop, look, and listen. Never proceed forward until you're certain it's safe to do so.
Use Quiet Weapons: When you finally do acquire some weapons, you'll want to get your hands on some silent ones. These are ideal for picking off lone zombies in order to avoid attracting a hoard. The best weapons for stealth kills as of now are the Crossbow and the Axe.
Lure Zombies into Buildings: You may have noticed this already, but zombies won't run inside of building. This makes buildings the ideal way to deal with or escape zombies. If you're able to defend yourself, then it will give you more time to attack them before they reach you. If you're unarmed, then luring them through a building will slow them down, allowing you to put more distance between you and them.
Day Z is definitely a game of experience. That said, it will take awhile to learn all the little tricks.
As a survivor in Day Z, maps play an extremely important role. This map (http://dayzdb.com/map) will show looting locations, as well as vehicle spawns, and can be used to navigate throughout Chernarus by using landmarks.
Looting: Stick to Barns/Residential Locations/Deer Stands while beginning your looting trips. These will provide weapons and even food/water. By sticking to smaller cities and heading north, you will typically avoid player contact completely. Before heading north, however, make sure you have a decent amount of water and food. Speed runs (also deemed suicide runs) into Cherno/Elektro can net you a decent amount of equipment, including the invaluable Map, GPS, Matches, Hunting Knife.
Note: If you have a map, you can Shift+Left Click to set a waypoint. This will show you the direction and distance from the target. This doesn't work on all servers, however.
Prepare to die. A lot. It's a steep learning curve to go from beginner to expert, but it's noticeable when you start to progress.