The forward "positions" aren't really set apart from faceoffs.
In defensive face-offs you should consider yourself first forward back and cover the low zone supporting the puck / containing the open opposing forward while your wingers go to their points.
However this can change when back checking if you are not the first forward back you'll want to cover your winger's point (the first one to your defensive end) while he plays low.
note: talk to your teammates about this though as you don't want them to think they shouldn't be going deep if they are the first forward back. and talk on ice if you guys are about even while racing back let them know which man you have and point out any open "trailers" (opponents coming in late looking for a bounce or drop) or where they should cover their point.
Offense and neutral zones again depend on where you've been shuffled to.
During Break out as the deepest forward in your zone most of the time you'd want to support the puck carrier.
Give your winger a short pass option in a different line than the far side winger (dont be in between them in a line).
Generally you'll be skating up in line with the near side faceoff dots trailing the puck carrier by only a couples steps just enough so if he gets jammed against the boards by a pinching dman you are able to help dig it out or cut off lanes in a turnover (as you'll be between the puck and your net).
Offensively only tips I can think of
-you might have a better view than your winger many times and because of that be vocal
-give your wingers a secondary passing option don't stay in a lane between your other 2 forwards as that will make it easy for a defender to cut both of you guys off from the play.
This applies to all 3 forwards but again you'll be a little more likely to be seeing the play rather than carrying a puck in the thick of it.
Best tip I can give you is during a faceoff make sure you are tying up the opposing centre and staying on him in the neutral or your defensive zone for the first steps (between him and the net stick on stick) as if he steps around you while everyone else picks up their man your opponents will probably end up with a scoring chance.
#1 - Cover the slot in the D zone. So important. When the defensemen are tied up with guys in the corner and/or there's a second guy in the slot, the center HAS to come back and get them.
#2 - Win faceoffs...this is underrated in rec league. Sets the tone for the entire shift and starts the momentum one way or the other.
#3 - Be able to skate. Typically they are the first forward on the backcheck but still have to join the rush up the ice, so being able to skate well and be in shape is key.
#4 - Good vision and passing ability. Centers often start the rush or make breakout passes from the high slot, and since they have wingers on either side most of the time, they've got to have the ability to see what's going on and set up their teammates.
I don't know what level you're playing, but based on the phrasing of the OP I assume you're in a beer/rec league situation. Everything below is written from that perspective.
One thing I found out early is that centers should be the most legitimately good all around hockey players among your forwards. So often I see guys playing there who have no business doing it, because they have winger teammates who are harder working and smarter and better skaters. Those teams lose a lot, because Mr. "I like taking faceoffs and touching the puck a lot" is still crossing the blue line while an opponent is scoring right in front of his goalie. A center who can't make it to the low slot at both ends on every trip up the ice is going to sink his team all by himself.
It took me a little while playing center to realize the importance of providing puck support for your teammates. Defensively you literally have your defenseman's back; you can't afford to drift around looking for guys to cover. Basically you have to play defensively as if you're in a 3-on-5, maintaining that triangular position and restraining yourself from rushing out to the point or corners (unless, of course, you're coordinated with your teammates in doing so). Not only will you force your opponents away from the slot, but the important thing I didn't realize early on, you will get a LOT more chances to start a counterattack. Being the second guy from the puck means you're the first passing option on a turnover. Again, bush league centers will go sprinting ahead rather than provide that important short pass for their teammates, which kills their teams' transition games and leads to even worse defensive efforts.
Offensively, it kinda depends on your wingers. If you have good skilled teammates who can create their own chances, life is pretty easy at center. Just don't turn the puck over and give your wingers the same level of support you give your defense at the other end. If you have to carry more of the offensive load, communication is hugely important. I would recommend telling your wingers to crash the net from the weak side, which means you always know where they are going to be if you run out of options and just need to put the puck on net. It's tough to be a playmaker unless you know where your wingers are, and beer league environments aren't the most coordinated situations.
The biggest takeaway: seriously, give your teammates puck support all the way up and down the ice. It's amazing how often the puck comes to you if you're simply staying in good position and providing proper outlet passing options.
I played center for the second time. Honestly, I'm ready for the other center to come back. The work isn't hard, but I'm having trouble pushing the play offensively, I was doing better as a winger, but maybe I just need more games under my belt.