Certainly check for leaks under the car, and look at the pavement where you park, but low fluid is a big cause of slipping.
To check your fluid level, find the section in your owners manual and follow the steps. I say that because each manufacturer might have slight differences, but in general, the steps are:
- Drive the car around neighborhood streets until the engine is up to normal operating temperature. This is to exercise the transmission in several gears and warm up the fluid.
- Park the car, apply the parking brake, and while your foot is on the main brake, slowly change into each possible gear with the shift lever slowly, pausing in each gear for a few seconds. Return the shift lever to Park.
- Open the hood, and leave the car running. Assume everything under the hood is too hot to touch, so test everything before grabbing. Also watch out for fans, belts and other rotating objects. Avoid scarves, necklaces, or loose clothes.
- Find the transmission dip stick, remove it, wipe it with a clean cloth, and put it back in. Pull it back out and read the level.
If it's low, you'll need to add it 1/4 to 1/2 quart at a time until the level reaches the correct level. Don't just dump in a whole quart unless you know it needs it. Transmissions shouldn't leak and they don't "use oil" like some engines, so it shouldn't be very low, if low at all.
Some manufacturers don't recommend checking your own fluid, because they're worried about the liability of a customer working on a running engine. That's a valid concern, so be careful, but as long as you are comfortable with it, you can normally do it on your own.