If you have a Dremel, you can buy an attachment with several types of 'stones' for sharpening tools, even your chainsaw blade(s)
Cora

If they are very old cutters, you'd do best to simply replace them. Most cutting tools, if not cared for properly, will eventually reach a point where a new edge just won't be possible. Next, if they are not bypass cutters - one blade passes the other during the cut - throw them in the trash and get the proper tool. Any trimmer that crushes - anvil-type trimmers - is the wrong tool for the garden.

You'll need a flat file. Never use a round one! Cora, that includes the Dremel. Sharpen the cutting edge first - long strokes, one direction. Then the opposite edge to remove any burrs. Don't wait until the tool needs sharpening, do this at least once a month, and oil the trimmers with vegetable oil not 3-in-one or WD40.

It was a flat file that he used. I just don't know how coarse it was. What number is the file that you use?

Get a second cut mill bastrd flat file and a handle to protect your fingers. File toward the cutting edge. Ace HW. Don't let it rust and it will last forever.

Here is a link that might be useful: flat file

uh oh. guess Dremel was just promoting a tool for us dummies! To be honest, I never saw my grandfather use anything but a file or a foot pedal-driven round stone to sharpen any of his tools. I remember he oiled them but couldn't say what type of oil.
cora

The safest oil to use is vegetable oil since you're going to be cutting plants with them.

Most knife-sharpening websites and videos say to wet your stone with mineral oil or water.

Yes, I think you could wind up with a sticky mess later on if you use vegetable oil for something like that.

Incidentally, the blue-handled one isn't for garden tools. They make special sharpeners for scissors (yellow handle) and one just for garden tools (green handle, I think), although I have no idea of what kind of job they do.

Mineral oil is good, too. But either one should be used very, very sparingly; you don't want to gum up the joint.

buy felco 912.............:)