Welcome to SOTA and the hobby in general, John.
Andy’s advice is sound - what I’ve put below is just my own spin on the same process. Joe is right - a spot put up with as long a lead time as possible helps to ensure that chasers are listening out for you.
I like to get on to the summit plenty early. I’ll set up, and pour a cup of coffee from the flask. While I’m drinking that I’ll have a flick around the band I’m about to use to judge what activity levels are like. If I spot a frequency I think I might QSY (change frequency) to I’ll listen for a bit to make sure it’s clear. If I don’t hear anything hear anything I’ll ask “Is the frequency in use, please? M0MYA portable”. Then I’ll listen for a few seconds more. At that point I’ll nip up to 145.500 (often called “S20”) and put out a CQ call. I’ll tend to make it fairly long so that people get a chance to hear me (e.g. if they are the other side of the shack, or perhaps they might have their radio scanning many channels, etc). It’s pretty rare not to get an answer on S20 from a not-too-remote summit, so once it comes in I’ll call the station who’s callsign was easiest to copy. If a lot come back, I’ll make mention of the fact so that people know that it’s going to be a bit busy, and hopefully they will choose to be patient. I’ll then ask the other station to QSY to my “working frequency”. Once there, I’ll ask again if the frequency is in use. Most times the other station will as well. Once you’ve both asked and both heard nothing then you can call the other station and start your QSO.
It sounds a lot, but that mostly just because it’s written down. It boils down to a few short “overs”. Once you’ve done it a handful of times if will become a simple process.
Let us know how you get on.
Good luck and 73,