If your baseboards are painted, you might need a straight edge razor to help you cut or uninstall them. In some cases, the baseboard is "glued" to the floor or to another wall by paint that dripped over the edge of the baseboard and dried on the other surface. You can remove this paint by scraping it with a straight edge razor. Do this prior to beginning any work on the baseboards themselves.
Use a small crowbar to pry the baseboard away from the wall once you've removed all paint from the edges of the baseboard. Put the sharp end of the crowbar in between the wall and the baseboard and hit the other end with a hammer until the bar wedges between the baseboard and the wall. Wiggle the crowbar until the baseboard separates from the wall. Repeat this step every six inches until the baseboard is loose all the way down the wall.
Use your bare hands to pull the baseboard off the wall once you've sufficiently loosened it. You can pull the baseboard out a little each time you loosen it or pull it off all at once. In either case, don't use too much force -- you don't want to damage the wall underneath the baseboard. If the baseboard won't budge, keep using the crowbar and hammer to help loosen it and then try to pull it off the wall again.
Once you remove baseboard from the wall, you'll have a bunch of nails sticking out from the wall that used to hold the baseboard. You need to remove the nails so they don't interfere with any trim or new baseboard you plan to put into the wall. You can either hammer the nails back into the wall or remove them from the wall using the other end of your hammer.