Select the ship by clicking on it. Then, tell it to move to a space occupied by a planet (right click on the planet to do this).

Edit: Looks like Kryo beat me to it.

no

I tried that once, Mistralok, and as I recall, it didn't work -- the source of the trade route was still the planet that manufactured the freighter.

Well, by golly, guys, you were right and I was wrong. I built a couple of freighters, sent them to orbit around other worlds for a couple of turns, then sent them off to start a trade route. The routes were both attributed to the planet on which they were built. It seems that a freighter is 'tagged' with the planet that they are produced on. I assumed (incorrectly), that that tag would be added when they left their last port of call. So- if a planet cannot manufacture a freighter, it cannot trade. Next time I'll try something out before talking out of...the side of my mouth.

Is it a custom designed freighter, or the core ship that comes with the game?

If it is custom designed, you may not have put a freight module on it.

I should probably mention...

If you are using Kryo's Hull System Mod, you may have inadvertently put the freighter module on as a piece of jewelry instead of using the correct module from the Modules/Capacity tab.

A related question - can I set up multiple trade routes between the same two planets? Is there any benefit or drawback to this?

Yep you can set up multiple trade routes between the same planets.