Parts you need:

•MINI Oil Filter (check to make sure it comes with the rubber o-ring)

•5 Qts Synthetic Oil 5w30 (BMW uses Castrol; Mobil1 is fine)

•36mm socket (yes, it's huge)

•13mm socket

•Wide oil pan & rags (you'll want a wide pan to avoid spillage)

•Pair of latex gloves (keeps hands clean and knuckles unscraped)

•Optional: Rhino Ramps (about $30 @ Wallmart)

•Bucket of spare cuss words (you'll want these for the last step)

Time to allot: about 25 minutes

Wrench, 36mm socket, 13mm socket, oil filter with o-ring, 5 qts Synthetic Oil

Step One: Prepare Car & Drain Oil

While you don't need to drive your car up on ramps to change the oil, I find that having a set of Rhino Ramps makes the job go faster. Also, Rhino ramps work with low-clearance vehicles and will not rub against the front air dam unlike other typical ramps. Once the car is on the ramps and the parking brake is set, locate the drain plug (it has a stripe on it and is just in front of the small fan. Using a 13mm socket, loosen and remove the plug and allow the oil to drain into your drain pan. Remove the oil cap from the valve cover to assist draining. Note: if you are using ramps, use a wide drain pan since the oil initially will pour out wide, then narrow as it finishes. Leave the pan underneath to catch the spillage from the oil filter. 

TIP: Loosen the canister while you drain the oil, which will break the seal and cause all the oil in the filter housing to drain through the plug hole. Otherwise, you'll have a bunch of extra oil seep out when you pull off the canister.

REPLACE THE OIL PLUG WHEN DONE

Step 2: Remove the Oil Filter

MINI uses a canister that houses the  filter insert, the same as many BMW's such the mid 80's 5 series. The canister is located just behind the valve cover; you can spot the large hex. You need a 36mm socket to remove the canister. I had to look for a socket in my auto parts store (Sears had one that was too deep), and since most 36mm sockets have a 1/2 inch bit, you may need a 3/8ths to 1/2 inch converter (unless you have a 1/2 inch socket drive). There is not much space to place the socket, adapter, and wrench, so you may want to buy a 1/2 inch socket drive and not use an adaptor.

You may wish to place a rag underneath the canister to catch the oil spillage. Twist the canister counter-clockwise and remove slowly, trying to turn the bottom towards the top to prevent the oil in the canister to spill. Drain the canister of oil and remove the old filter. Using a rag, wipe the inside of the canister to remove any gunk.

Prepare and Install the New Oil Filter

The new filter comes with a rubber o-ring. Remove the old one from the canister and replace with the new one, taking your finger and wiping a bit of oil around the circumference of the installed o-ring.

MINI filters have a rubber seal at one end with a smaller hole, and a larger hole with no seal at the other end. The larger hole goes against the inside bottom of the canister, and the end with the rubber seal ends up going flush against the engine. But first you have to prep the filter by enlarging both of the holes at either end to ensure the canister fits on easily.

You want to first prep the rubber seal side by forcing it on the engine block first, then removing it and forcing it on the canister. The middle picture shows the fitting on the engine block, you can just make out the small round pipe-like fitting. Once you have pushed the filter against the engine block, remove it and place the it in the canister, with the rubber seal facing out. By forcing it in the canister, you'll also enlarge the larger hole as well.

TIP: Some report good luck in first pushing the filter into the canister, then removing it and pushing the filter against the engine block and screwing the canister on over the filter. 

Now here is where you make use of that bucket of cuss words. The engine block has a spring loaded piece that pushes up against the filter. Getting the canister threaded back onto the engine block takes patience and several tries. I got through the D, S, F words and had to combine the F and S words together before I got the canister/filter to thread on the engine block properly. Here's my trick:

I push the canister firmly against the engine block as I am just starting to thread it. I rock it gently back and forth until I can sense with my fingers that the canister is threading correctly. Then I continue firmly pressing the canister while tightening it by hand. You can hand tighten it almost all the way, and maybe only need a 1/2 turn of the socket to finish tightening it.

You know you are not threading correctly when after 1 turn or so, the canister won't turn. You can feel with your fingers that the canister is threading at an angle. Start again and dip into your bucket of cuss words.

If after 3-4 tries you can't seem to get it threaded, remove the filter from the canister and try threading an empty canister on just to get the feel. It takes about 5-6 turns to completely tighten it.

Finally, ensuring that you put the oil drain plug in and correctly tightened the canister, add 4.7 quarts of synthetic oil and tighten the oil cap. Clean the spilled oil off the engine block and recycle your old oil at a local gas station or auto parts store.