It helps for me to think of the game as phases, each dictated by the circles. First phase is gear collection / survival when you'll be getting as much kit as possible and surviving the first cull. Choices here are to play full on deathmatch by jumping somewhere popular in the flight path and just have a blast (survival chances slim because its random whether someone lands behind you/gets to the shotgun before you, and in this phase shotgun is king) or gamble on a long range jump and find a vehicle driving far out of the flight path to have some quiet looting time. You need to know where to go - generally built up areas and look for tall buildings - park your car out of the way then run through them like hell, closing the internal doors and the ground floor doors you open (anyone arriving will think no one is inside and barge in giving you a chance to hear them arriving and avoid the nasty surprise). Keep an ear out for approaching vehicles and keep in mind that with every second more players are arriving in the area.
Second phase is your running to the second and third circles. You could just drive straight to the centerpoint and camp... but be warned. This may sound like the easy option but its fifty fifty whether youll be driving straight into the sights of someone already camping. What i love about this game are all the little dramas that play out before the final whistle, and the battle for the center ground happens very early and consistently at each contraction, usually amongst experienced players who are very well armed - who basically feel there isnt any point playing the edges game and just set up with their sniper rifles and 8x scopes. This truly is a whole game in itself especially in the cities close to the center. Even then, you wont know which way the circle is moving so you'll have to keep fighting these battles at every shrink, except of course you also have the edge players arriving so youre trapped in a sandwich of campers and armed to the teeth players running in.
If you do play the edges then your primary purpose is to rack up kills. Hunt for good loot (AR/Sniper and 4x scopes - the SCAR with all the attachments is most popular currently) and stay out of buildings. Set up camp (on top of buildings with a ledge and lie down, dont squat - your head is visible at range) at every contraction edge and wait until the circle has closed completely, have one more scan for people running in from the blue which is quite feasible in the first two contractions, then start running for the next circle. Situational Awareness is your best mate, bind the freelook key to your mouse thumb and be constantly scanning in all directions when you're running or stopped. Dont take the hopeless shots from miles away unless you are absolutely certain of hitting or you have a silencer. In fact, dont give away your position unless you are certain of a kill or a situation is emerging that leaves you no choice. Never give up the high ground, but never be on a peak - you can be seen for miles. When you shoot aim low and aim for the head with scopes directly ni the center. Forget the increments, by the time you start getting good at sniping youll have figured those out.
The final circle is pure chance. I play the edge and only run at the very last second, but if youre running into someones sights thats pretty much with the Gods. One thing i do like is wheat fields. Lie down in those and you are pretty much invisible.
Always remember the third person peak! It works for you as much as against you, but if you try to close on somebody who has the advantage, for instance they are behind a wall and you have to cross an open space to get to them, you are dead meat as they can choose when to pop out and shoot you as you're running. If you get caught in a shoot out - look, heal, retreat and flank.
Anyway, thats it, have fun!