Hola dude. As the owner of a '70 250CE I'll be happy to guide you through this.

Supplies
-6ish quarts of oil. My 250 loves Castrol "high Mileage" 5w40.
-Socket wrench with extension. I Think the socket you need is an 11/16 or somewhere close to that. I'm not going to go climb under the car though because it's early and cold.
-New Filter (get the best you can)
-Oil Catcher
-Floor Jack and 2 (TWO) safety jacks. Never let just a floor jack hold your car up. Always have two secure safety jacks holding the car up.
-Funnel, or intense pouring zen concentration.

So, first step is to make sure you have the car warmed up a little. It doesn't have to be at operating temperature because you dont' want to scald yourself. Just warm it up a little so that the oil picks up sediment and drains a little easier. Then jack up the car. Once you have it safely on jack stands, open the hood. Then, open the oil cap on top of the engine, It's on the top dead center.

Now, slide the oil catcher under the oil pan of the engine. Now would also be a good time to slide your socket wrench under the car as well. Bring some paper towels if you're clumsy. Next, use your socket wrench to remove the drain plug on the oil pan. It faces the rear of the car. Get it most of the way out with the socket wrench, then start turning it with your hand. Make sure that the oil will land in your catch pan because cleaning up oil spills sucks.... a lot.

Once you have oil draining into the catch pan, it's time for a little breather. When the oil is just barely dripping into the catch pan, it's drained as much as it's probably going to, but you can leave the catch pan where it is while you remove the filter. When you're under the car, facing up at the engine with your legs sticking out in front the oil filter is going to be on your left (drivers side.) It's a silver can thats larger than a regular beer can, and about the size of one of those big beer cans, like a travelin' beer. It's secured via one long bolt that goes through the center. You'll probably need an extension on your socket wrench.

Find a way to work your socket wrench and arm into position, and remove the filter cannister. Take note of what everyone else said concerning gaskets. Be aware that oil will drain from the filter, and it's probably going to land directly on your suspension before makig contact with your catch pan. Obviously it's important to catch the oil from the filter. Be careful not to scald yourself on the engine block if you were a little too enthusiastic warming up your engine. Pull the old filter out of the cannister and disgard it according to enviornmental regulations in your area. This means don't just chuck it in the garbage can. Think of the baby seals... and the blue titted booby foot bird. Or something.

Anyway, place the new filter in the cannister, and refitting is the opposite of removal (Don't you love when Haynes manuals say that about something like a rear diff?) Getting the cannister and your socket wrench into place can be a little tricky, have patience and try new ways if you're getting frustrated. Again, be mindful of your engine block as it may be hot.

You can also drain the oil cooler which is advised as it can contain a lot of dirty oil that you dont' want to mingle with your fresh oil, especially if it's a different weight. To drain the oil cooler (it's in front next to the radiator, it looks like a narrow radiator) simply unscrew the drain plug on the bottom and let it drain into the catcher as you did with the engine oil pan.

Make sure your filter, engine oil drain plug, and oil cooler drain plug are properly installed (tight, but not insanely tight. If you're OCD your Haynes manual will tell you the exact torque.) It's time to stick the funnel in the oil cap on top of the engine. Begin filling your engine with your chosen oil, make sure to pour out of the container the right way (There's a picture on the side of the bottly.) because air bubbles will gurgle out and might splatter the oil if you hold the bottle upsidown.

If you can, measure how much oil drained into the catch pan you used, Lets say you have 7 quarts in the catch pan. Assuming your engine oil was at the proper level before you drained it, then you should add 6.5 quarts then run the engine for a moment before checking the level (engine off when you check) and topping up. Replace the oil cap when you're oil is at the right level. Clean up your work area, and let the car down.