It's often educational to see how other people do this. I see a few general trends.
Up and down arrows on every row. This is horrible and should in my opinion be avoided, since it handles multiple clicks very, very poorly indeed. However, as a drag-drop hint it could work:
OneSync (drag-drop hint):
Sdevireddy (this one shows in an animated fashion why this is terrible UI: to move something up multiple rows, you have to click and reposition the mouse for each row to move up):
Then there's the arrows-to-the-side method:
Then there's the way everyone and their dog does it: Internationalized "Move Up" and "Move Down" buttons. With words on. So people actually know what you mean.
Then there's plusses and minuses. I could find exactly zero examples of this in the wild, which is a good reason to wonder whether it's the right thing to do.
On the other hand, if it's a thing you MUST do, we can see something else from the above examples: button position matters.
If you have the '-' button above the '+' button, then '+' will be interpreted by the user as increasing the selected item's position number within the list; moving it down from position zero.
If you have the '+' button above the '-' button, then '+' will be interpreted as moving the selected item higher in the list; moving it up towards position zero.
Either of these is a valid way to do it. I'd personally go for plus-on-top, but the most important part is what position the buttons are in.
given than your primary cue is button position, you don't even need to have plus and minus. You can have a camel icon, and a banana icon. If you have camel above banana, appropriately vertically-centered to the right of the list, then "camel" will be guessed to raise the item up in the list. Users will just assume there's some reference they're missing.