To trade:
Visit the team you want to trade with, there is either an option to trade on the team page or the player you want to trade for. You should be able to get a pre assessment of the trade outcome too. It's not a slam dunk of course, the other person needs to agree and the rest of the league can still reject it (rarely happens, was put in place following trade gate way back when - right Rob!).
Free Agents:
Visit the player list, pick the player you want to add, select the player you want to drop and voila. If it's a waiver, you'll be subject to your claim priority. If someone with a higher priority selects the same player then you lose. It's normally a couple of days process.
Sure someone else can add any bits I may have missed but that should cover most of it