First, you choose the LT that you wish to upgrade, or "star up." Let's say you choose a 2* Blink.
Second, you choose two other LT's to fuse into your new cool higher LT from step 1. They must be the same type (common, uncommon, rare, epic) as the first LT, and have the same number of stars. For example, do fuse a 2* Blink into a 3* Blink, you'd need 2 LT's who were 2* uncommon.
Third, you fuse them. This consumes a recombinator, and the 2nd and 3rd LT.
As easy as 1-2-3, right? But sometimes you get an error - "You don't have enough Lieutenants" even when you do, right?
The following LT's cannot be fused away:
You can't fuse your last one. If you have a 2* and a 1* you can fuse one of them, but not both.
When I suspect that I might have some fusing possibilities, I just pick any LT with the stars and type I want, and choose to fuse them. If I can see more than one LT on the next screen, I know that fusing is an option - that I have a recombinator and enough LT's. It won't show you LT's that you can't fuse away. Then I cancel out and start over if I want to actually complete a fusing, using the specific LT that I want to build up.
Whether fusing is wise or not is a different matter. I seldom buy crates, so I'm often willing to fuse the crate LT's away, since they won't ever be strong enough to seat.
Or will they? If you have Centurion, or Victoria, you might want their skills, and be willing to wait to fuse them up. I would like to have a 6* Eve Armstrong, that's a rolling ball of butcher knives right there.
A common guideline is never to fuse away the last of any LT. That keeps the number of LT's high. I kind of agree with Voodoo though - if you're not using it, you're wasting it. When are you using an LT that you never seat? Um, boss jobs. They can give you LT criticals. So think carefully before you fuse - then try the old 1-2-3.