One of the keys to arbitration is WHEN people go to arbitration. For rookies I think they are eligble for arbitration after I believe three years of service ( they are not eligible for free agency until 5 or 6 years of service). This is why you see young players who are very good sign deals for much less than some of the older free agents ( the A's do this quite alot and did this with Zito, Mulder and Hudson) and these contracts carry them through their 'arbitration eligible years' until free agency.
When a Major leaguer become a free agent, the team he plyed for the previous season has the option of offering them arbitration, and as was previously said the team and the player submit salaries they desire and then argue in front of an arbitrator as to why their salary should be what they offered. The player can decide NOT to accpet arbitration and then becomes an unristricted free agent. They can negotiate with their team for about 30 days exclusively after declining arbitration, but if they fail to reach an agreement, they cant sign with that team until May 1st. After the negotiating period, they are free to sign with any other team, BUT the team who offered the player arbitration gets a draft pick from the signing team.
I think that about covers it.