Generally if you are on a known good coverage system there is no need to ask for a “Radio Check” or “Signal report”
A better practice is to simply LISTEN to a conversation on the repeater for a little while. If you are getting good signal from the repeater then you will most likely be able to hit that repeater with your radio. In general it is not a good radio practice to use a hand held radio inside a building and expect to reach the repeater reliably.
After you have listened for a little while you can join a conversation by waiting for a pause between the people talking and then key up and say “comment” or “question” and then WAIT to be recognized. You should only do this if you really have something to add to the conversation, if you are only going to reiterate what someone else is already saying, save that for fakebook and twitter comments.
A better choice if you are new and want to just see how your radio is doing is to wait until the frequency is clear, by listening for at least a minute, then say something like “this is (your callsign) listening”. In most cases someone will respond to you and you can have a conversation. IF you are not making the repeater someone will likely say “station calling you’re all static” or something similar. Then move to a better spot or try a different repeater.
If you have been on a known good coverage system for a while and recently got a new radio there is NO reason to ask for a “radio check” or “audio report”, just use your new radio. If you key up and don’t hit the repeater that has always worked fine for you then you probably programmed it wrong.
Sometimes there are good reasons to transmit and ask for a “radio check”. For instance if you are preparing for an event like a race or parade it is common to request a radio check once you get to your assigned position.