I never remove base molding because there is too much chance of breaking it and/or damaging the wall. But if there is quarter round or base shoe in front of the base molding, that must be removed.
When laying the tile, do not grout around the edges; leave a gap, and cover it with base shoe or quarter round. If you do not, you could cause the tile in the center to buckle up from expansion/contraction.
But there is a lot more to setting tile, starting with the base or backerboard. Visit my website at www.bobf.info for some guidance.