The draft is really just another part of free agency, except you do not have to worry as much about how much a player will cost, and you know when you are going to pick. The draft provides teams with good young talent, and once you know who you are going to draft you are then free to see what other needs you have.
Teams often have different strategies as to how they like to build their team. Some like to build through the draft, finding good young pieces and then bringing in veteran free agents to fill in the gaps.
A good example of this would be the Washington Capitals. The Caps had several good draft years in a row, drafting players like Alexander Ovechkin, Alexander Semin (currently an unrestricted free agent), Nicklas Backstrom and Mike Green. These players are now the foundation of the franchise.
Some do the opposite, preferring their core to be made up of veterans, helped out by the young guns they draft.
Whatever the case may be for your team, know where they draft, how many picks they have and who their looking at picking. That will give you a good idea of what they are going to do in free agency.