Water oozing out around the base of a toilet usually indicates a faulty wax ring, which, on most types of toilets, seals the junction between the base of the toilet and the waste pipe (called a closet bend).
Before you start a wax ring replacement, buy a new wax ring, available for a few dollars online or at a home improvement or hardware store. The type with a rubber collar is less likely to leak than a standard ring.
To replace the toilet's wax ring:
1) Empty the water from the toilet. To do this, shut off the water supply valve behind the toilet, flush the toilet, and re-flush to drain most of the water from the tank and bowl. Sponge out the remainder. Disconnect the water supply from the valve.
2) Remove the plastic covers from the anchor bolts that secure the toilet to the floor on both sides of the toilet bowl. If necessary, use a screwdriver to pry off the covers.
3) Next, turn the closet flange nuts counterclockwise, using a wrench, to remove them. Also remove the washers and set this hardware aside.
4) Gently rock the toilet from side to side and back and forth to break its seal at the base. The next step will be to lift it up and set it aside--you might need some help for this because a toilet is typically heavy. Lay it on its side so you don't damage the bottom or mess up the floor with the wax that may still be on the base. Beware: The toilet may still contain water.
5) Seal the mouth of the floor drain opening by stuffing a rag into the top of the pipe to prevent sewer gasses from entering the bathroom.
6) Use a putty knife to remove the old from the floor flange and the toilet's base. Then press the new wax ring onto the toilet's drain cowling, collar pointing away from the bowl, following the package instructions. Put a small bead of caulking compound around the perimeter of the toilet's base.
7) Pull the rag out of the drain pipe. Then, with a helper, lift the toilet up, center the cowling over the drain, and lower it down onto the flange, guiding the bolts through the mounting holes. Note: You want to position it right the first time because you can damage the wax ring if you miss. Here's a tip: Push large drinking straws onto the mounting bolts to help guide the holes in the toilet's base.
8) Put the washers and nuts back onto the closet anchor bolts and gently snug them down with a wrench. Do not over-tighten--this can crack the porcelain! Replace the plastic bolt covers. Turn on the water supply to refill the toilet tank, replace the tank's lid, and then test for leaks around the base by flushing the toilet.