How do you fix a manual transmission that is leaking?

The most probable place that a manual transmission could be leaking from is at the drive axle seals. In this case I don't believe that the transmission would have to bo taken down, but the drive axles will have to be pulled from the transmission in order to change the seals.

The seals around the drive axles need to be replaced. When you replace them, check the surface of the drive axle where the seal was in contact. Is it rough or worn down? If it is rough (damaged or not properly ground during manufacturing) you will probably get a leak again. If it is worn down too much, you will probably get a leak immediately.

When you pull the axles out of the transmission/transaxle, be ready for gear oil or transmission fluid to start pouring out. Have something ready to catch it. Be careful when removing the old seal to not damage the surface where the new seal will go. When you press the new seal into place, ensure that you do all sides evenly at the same time. You can to this by tapping gently all around the seal as it goes in. Generaly try to do it evenly and not any one side too much more that the others. Putting it in crooked can cause it to get damaged and lead to leaks.

I recently replaced one of the seals in my transaxle. The instructions told me to coat the inside with bearing grease when installing it.

If your transmission is not leaking around the axle seals, it may have a leaking gasket that needs to be replaced. Again, be ready for lots of fluid to come spilling out when you break the seal of the gasket.

Another location for leaks is the input shaft of the transmission (near the clutch). The input shaft has a seal around it.

A less likely location for leaks is around the shift linkage. Since the linkage is usually on the top or upper sides, you will seldom get leaks there.