Easy, Illustrated Instructions on How to Change your Oil and Replace the Oil Filter in a Car
If the bolt is very tight, use an extended socket wrench, or a socket handle extension to apply more force. Bolts unscrew counter-clockwise, but if you are squeezed under a car, looking at them from the stem side, it can be confusing as to which direction is actually counter-clockwise.
I use an 18" piece of metal tube (conduit) as a socket handle extension. It works.
Once the bolt is loose, put an oil pan underneath to catch the oil which is going to fall in a minute. There will probably be about a gallon of dirty oil coming out, so you can't use a soda can or a pie plate. Also, the car is probably too close to the ground to squeeze a normal bucket under there. You could use a disposible broiler pan from the dollar store. If you go to the dollar store, you might as well get some rubber gloves too.
As you twist out the bolt, the oil will come out like it is being sprayed out of a garden hose. Get out of the way.
You can try to hold onto the bolt so it doesn't drop into the used oil, or you can let it drop in and fish it out later with a spoon or a magnet. Either way you are probably going to get some oil on your hands.
Let the oil drain for a few minutes. If your oil pan is wide enough to catch oil dripping from the oil filter hole too, slide the oil pan over so that it is aligned under both drip points. Grab the oil filter with your hand and try to twist it loose. It comes off counter-clockwise if you are viewing it from the closed back of the oil filter.
Sometimes the oil filter is situated in such a way that you've pretty much got to remove one of the wheels to get your hands onto the oil filter.
If the oil filter is on too tight, there are a few things you can try to get it loose. You can buy an oil-filter wrench, which will wrap around it like a pipe wrench. If your grip is slipping, you can wrap a few rubber bands around it to provide a better grip.
If your problem is that your body is in a strange position under the car, you can wriggle around to improve your position. Another tactic is to stab a screwdriver sideways through the filter, giving yourself a big handle to twist it with. This will destroy the filter, but you are going to throw it away when you get it off anyway, so it is a valid approach. There is no "undo" to fix the pierced oil filter if something else goes awry in the oil changing procedure.
The filter is pretty much a cup full of oil, so try to get it upright as soon as it comes off of the car. Check the placement of your oil pan as this second stream of oil drips from the engine.