Allow at least two days for your tile grout to dry completely. While it is not absolutely necessary, if your baseboards are unpainted it may be wise to apply primer before caulking so that the caulk does not get stuck to the wood grain.
Fill a caulk gun with caulk that is a blend of acrylic and silicone. Hold the gun at a 30-degree angle above the baseboard crack and squeeze the trigger.
Squeeze out enough caulk so that it rests slightly higher than the baseboard and slide the gun slowly along the baseboard as you work. Cover 24 inches at a time.
Use your finger to smooth out the caulk line. Wet a sponge and then wring as much water from it as possible. Run the sponge over the caulk line to smooth it out and remove any excess that still remains. Take care not to apply so much force that you dig caulk out of the crack.
Use a putty knife, when necessary, to lightly scrape caulk from decorative notches at the bottom of the baseboards or the surface of the tile.