Changing the oil and oil filter in your car is necessary to keep internal engine parts lubricated with clean oil. Changes are performed at intervals of time which may vary depending on the vehicle and conditions.
I will outline the basic task with some basic slip ups and some tips to help you do the job right.

PREPARATION:
First and foremost, refer to your vehicles manual to find out what the manufacturer recommends. If you don't know, you can find this information online or at the parts store. 
Locate the engine oil filter and the drain plug and oil filling hole. 
You will need an oil pan to catch the oil. Make sure it is low enough profile to fit under the vehicle.
You will need a ratchet and socket to loosen the drain plug. It is important that the socket fits the drain plug exaclty, and important not to overtighten or crossthread the drain plug.
You will need a large funnel to place into the oil opening. The proper sized and design funnel can really help you out here. Make sure the funnel is stored properly and kept clean. Always inspect it and clean any debris before using. 
You will need an oil filter wrench. I recommend the pliers kind. Although you may not need to use them when installing your new filter, if you have a good grip hand tight is okay, you may need to use it to remove the old filter. Don't waste money on cheap designs. Get the pliers kind. Not being able to get the old filter off is something that can slow down the whole procedure. 
You may also need a floor jack to raise the car, depending on the vehicle. If you do, you will need to research lift points and how to safely raise your vehicle.Usually the oil can be changed without raising the vehicle. Find where everything is, see if you can reach it, and make sure your drain pan fits underneath. I can do a Toyota Camry without raising it. 

i'm still working on this