I'm still a beginner in this area, so take this answer with a gran of salt.
I've had a chance to see a ham test repeaters few days ago, so I'll describe what he did:
First and the most obvious, make sure that the transmit and receive frequencies are correctly set on the radio.
Go to frequency of interest and listen for a while. If there is a conversation going on, wait until there's a natural gap in the conversation and then announce your presence. A simple:"This is
CALLSIGN testing link with
repeater name. Can anyone give me a signal report?" seems to do the trick. If the crowd at the repeater shows interest, share some more information about your rig with them.
If it looks like there are no users at the repeater, use the same procedure as if there are other users. You don't know if someone may be just listening to the repeater. If that's the case, you may receive a response even if it looks like the repeater is deserted.
If there really aren't any other users at the repeater, then your experiments probably won't bother anyone. Repeaters, here in Serbia at least, keep transmitting for a few seconds after you finish transmitting. If you have an S meter, you can see if your transmission triggered the repeater. If you really want to have a signal report, you'll probably need another radio. If you're lucky, there could be a WebSDR station within the range of the repeater. Otherwise, you'd probably need another receiver. One thing you could try, depending on the friendliness of local hams, is to ask someone on some other frequency to listen to the repeater and give you a report.