All MLB teams have their Spring Training in either Arizona or Florida. Pictures and catchers are the first players to arrive and most teams will display a message on their website stating when they are scheduled to show up. The rest of the team usually comes in about a week or two later. However... this does not mean that position players can not show up early. The crowds are generally smaller at the beginning of Spring Training and many players who are looking to get a jump start on the new season show up early, so if you are out there, you might get lucky.
Best tips and tricks to get autographs:
1) Go during practice and get there early. If practice is scheduled to start at 10am, get there at 8:30am or sooner. You should be able to beat the crowds and may be able to catch a player going to workout before practice. I've heard of players showing up as early as 5am, when practice didn't start until 10am.
2) Always ask the field staff about the best and appropriate places to get an autograph. The team may have designated or "un-designated" areas for fans to get autographs.
3) Follow the crowd. When a player decides to stop and sign, everyone immediately takes notice and there is usually a swarm of people. When you see a good size crowd, that means someone is signing.
4) Stay an hour or two after practice. The players are done for the day, the crowds have died down and the everyone is heading home... except you. This is the last opportunity of the day to get the autograph you want. Ask the field staff to see what part of the field the players will be leaving from and where the best spot to get an autograph would be.
5) Be patient. The players are out there because it is their job and they are training to bring home a World Series Championship for you, the fan. Harassing a player for an autograph can irritate him, meaning no autograph for you and possibly get you expelled from the grounds.
6) Not all players sign autographs, so do some research on the player(s) you want before you leave the house. Ask other fans to which players do and don't. It can be very disappointing, if you have traveled a long ways, got to the field early, stayed late and then find out that the guy you wanted doesn't sign. It is each players decision whether they decide to autograph your item, or not.
7) Many teams have a FanFest, which is a great opportunity to get autographs. Not all players are required to be there, so check the schedule ahead of time to see which players are scheduled to be there. You'll need to purchase an autograph ticket, which will give you access to the autograph booths. Current and former players are there to sign your item.
Above all, have fun. Take in all the sites and sounds of Spring Training. Enjoy the upfront and personal access you have to the players. This is where every baseball season starts.