Ideally a typical repeater when you stop transmitting will have a short delay, the courtesy tone (it's courtesy to wait for that tone so that other people can get a chance to break in), and then another delay, and then they drop carrier. In an ideal situation, you should be able to hear that tone, and rely on weak reciprocity -- if you can hear the tone clearly, there's a good chance you got into the repeater clearly.
However, lots of things can go wrong with that. Some repeaters leave out some or all of those delays, and then you have to get lucky that your radio's transmit to receive transition is fast enough to catch some part of the tail of the repeater's transmission. Some of them leave out the courtesy tone too, and then it's guesswork if you got in at all.
Also, some repeaters are not well balanced on receive sensitivity vs. transmit power, so the reciprocity might not be there, as maybe the repeater doesn't hear was well as it speaks (or vice versa). You might be strong enough to key the repeater but not enough to get a clear transmission into it.
A few repeaters have a repeat delay, so that if you speak and then unkey quickly, you might catch the tail of the delayed repeat of your transmission. (This might be half a syllable or so.)
A very few rare repeaters have instrumentation in them that can actually measure your signal strength and report it back to you. This is obviously more reliable (and really cool). Typically this is triggered by some touchtone sequence that might be published.
A few more repeaters are able to actually record what they hear and when you unkey, repeat it back to you. Any repeater with echolink or IRLP capability can do this. Usually repeaters like this have their touch tone sequence to active echolink or irlp published, and the internet test reflectors are published in their respective documentation online.
And, all of that failing, your best bet is to call out for a signal report and see if someone will respond and let you know what they hear! Many repeaters have members who can give you a technical description of your signal quality that might be very helpful. You might even want to try this as a first approach, and introduce yourself while you are at it.