The mouse I will be using for this is a Microsoft Intellimouse Trackball from 1998. This tutorial will work for any other trackball mouse that is made before ~2004. Most made after that don't use the same sort of mechanism.
Step 1: Find and Turn Retainer Ring
You can see a small notch or dot on the ring and one that lines up with it on the body.
Turn the ring counter-clockwise as far as it will turn. The notch on the ring will then be about 30-90 degrees from the notch on the body.
Step 2: Remove the Ball and Ring
If it does not fall out, tap the ring and ball while its upside down, and make sure the ring is all the way turned.
Step 3: Clean the Main Rollers
Take a wooden pencil with a very solid pink eraser. The really cheep ones that have stiff pink erasers on them work best. If you use one with a crumbly eraser you will do more harm then good.
Use the eraser to clean off the roller (the black part of it) by moving the eraser from side to side on it while turning the roller with your finger. The roller in the picture has been recently cleaned so its nice and black but yours will be grey and nasty
Do this for each roller then turn the mouse upside down and tap it to get all the dust and lint out.
Important Note: The rollers can be kind of delicate so take care while cleaning them.
Step 4: Clean Strings and Lint Wrapped Around Axles
Take a small tweezers and very carefully pick all the lint and strings off of them. The axles are very thin and can be easily bent so be very very gentle. There will also be a small wire spring on each side so be careful not to touch that.
Again the one in the picture is clean, but yours will have a good sized glob of dirt around it.
After you do that, turn the mouse over and tap it to get the lint out.
Step 5: Clean and Lubricate Bearings
Do not remove the balls, If you take them out you will lose them, and its impossible to find replacements for those things.
Use your fingers or a Q tip to wipe of the dirt from around the bearing.
Rub a very small amount of Vaseline on each ball. This will make the ball spin nice and free. Its important to not get any on the rollers or other parts of the mouse as it will keep the main ball from turning the rollers. This is also why its important to apply a very small amount.
Tip: If you have no Vaseline, take a "Chapstick" and rub a bit on your finger, then apply it to the balls the same way you would the Vaseline.
Step 6: Cleaning the Main Ball
Take the ball and wash it under the hottest water that will come out of your faucet.
Dry the ball off with a cloth, or let it air dry.
The ball must be completely dry before you continue on.
Step 7: Putting It Back Togather
The ball should turn nice and smooth now, and it will track just like it did when it was new.
I hope this helped you breath some life back into one of these things. I like mine much better then new mice even though its 14 years old.