The first question that needs addressed is "Where do I look to check my fluids?" That all depends on your vehicle. The locations of your fluid reservoirs and dipsticks should all be detailed in your vehicle owner's manual, but if your manual is missing, or doesn't clearly explain this, a Haynes manual will, and is always a good option. In fact, a Haynes manual and a bit of ambition can save you substantial money on basic automotive repairs, if you're so inclined.
Beyond that, what fluids are we checking, and what are we looking for?
OilOil should be clear and golden or amber in color. If it's black, you're very likely due for an oil and filter change. If it's cloudy and the color of chocolate milk or coffee with creamer, you have a serious engine issue that needs addressed immediately.
CoolantUsually (but not always) a bright, fluorescent green in color, your coolant is almost always mixed 50/50 with water. It can be purchased from the parts store in either premixed or unmixed condition, in gallon jugs. Just be aware of which you're purchasing, and make sure it's mixed to the proper levels before you put it in your engine. Some newer vehicles use a different coolant, so if you're not sure, ask at the counter before you buy. They can almost always look up the specified coolant for your vehicle.
Most vehicles have coolant in the radiator, as well as an auxiliary tank nearby. The auxiliary tank will have markings for a full coolant level on the side. Coolant should be checked when the engine is cold, particularly if you're removing the radiator cap to check or top off. Your engine's cooling system is under pressure, and if the cap is removed while it's hot, steam will come out, quite violently, and can cause very serious burns.
Transmission FluidThis is only applicable to vehicles with automatic transmissions. This is another item with a couple vehicle-specific needs, so ask at the counter when you buy, or check the specification in your owner's manual. The majority of transmission fluids are bright red in color (there are a few that are green-hued). If your fluid is black or brown, or smells burnt, your transmission is in need of service in the very near future.
Brake FluidBrake fluid is contained in a sealed reservoir, usually on the cab-side of the engine compartment. This reservoir will have Max/Min markings to let you know your fluid is within acceptable levels. As your braking system is a closed system, it should not burn/consume fluid. A level that shows as too low on the reservoir can indicate worn brakes, or a leak in the system. Either is an issue that needs addressed in short order.
Washer FluidNot a fluid that will cause engine failure if it runs dry, but being able to see out of your windshield is kind of nice. Sold in gallon jugs, just fill the reservoir. There are variants with a de-icing agent, which is particularly handy for those of us in places that have winters that get cold and snowy.
Keeping on top of just a few basic items like this can save you from some... interesting... misadventures, and help catch small problems before they become big, expensive problems.
Stay safe out there.