Scratch the surface of the seed if it has a hard seed coat (such as you would find on a bean or pea seed). You can do this using a sharp knife, a pin, or a piece of sand paper. If using a knife, make a small, shallow cut at the end furthest from the "eye" of the seed. For a small seed, use a pin to poke a tiny hole. You could also use a piece of sand paper to make some scratches on the surface of the seed. All of these methods will allow water to penetrate into the seed more quickly, causing faster germination.
Put the seeds into a bowl or pan of warm water. If you have several different kinds of seeds, you might want to use a foam egg carton and empty a seed packet in each section. (Don't forget to mark the sections so that you know which seeds are which!) The temperature of the water can be hot starting out, but not any hotter than you can stand to have running on your hand.
Add a small drop of dish detergent to the water if you want to speed the process even more. The detergent will reduce the surface tension of the water, allowing it to penetrate the seed more quickly. (The detergent is optional. Soaking works even without it.)
Soak the seeds overnight, or at least for three hours. The tougher the seed coat, the longer the seeds will need to soak.
Instead of soaking the seeds (or before soaking), you could try heating them. Heat the seeds in the microwave, using the lowest power setting. Use four 15-second intervals with a 30-second cooling time in between.
Plant the seeds in soil right after soaking or heating, or else place them inside a plastic baggie along with a slightly damp paper towel.
If using the baggie method, hang the baggies near a window where there is plenty of indirect sunlight and check them each day. When the seeds in the baggies have sprouted and you can see a root and a stem emerging, plant them in dirt (with the root side down, of course).
If you want to keep hurrying the seeds along, you can add plant food to the potting soil (unless the potting mix is already enriched). Follow the directions that come with the plant food.