Strip away old paint with the mineral spirits or other paint stripping liquid. Dab the mineral spirits onto an old, but clean cloth and rub it along the grain of the wood. If you can't see the wood grain, that's OK, just use the same direction for each application.
The older the table, the more coats of paint it may have. Strip all the way through to the base wood.
Fill in the nooks and crannies and nicks of the wood with wood filler. Use a wood filler that matches your wood--test it in an inconspicuous area of the table first if you are unsure. Use a small trowel or putty knife to insert wood filler into cracks and holes. Smooth over completely before allowing to dry.
Allow to dry completely before moving on to Step 3.
Sand the entire table. Wipe the surface with the tack cloth, which is specially designed to absorb dust, to clear the table of all sanding and dust particles.
If there are parts of the table you do not wish to paint--for example, if you are creating a design or using multiple colors--cover them with painter's tape.
Prime the table with a base coat of paint primer. Use an interior latex primer designed for wood, as opposed to one designed for masonry or metal. Allow to dry completely.
Paint. Go for one solid color, or stripes, or polka dots or any other design and colors you choose. Match a newly renovated room or update a child's table with a more grown-up solid color. If painting multiple coats, allow to dry completely between coats.