you will need to tell us your location; it will vary greatly across the world.
In the UK, for me, diagnosis wasn't too hard via BUPA - my phsychiatrist seeing me for my other mental health problems recommended me and it was relatively quick to get an ADHD diagnosis; now, however, I am stuck - there's a UK shorage of medication so my psychiatrist is unwilling to proscribe for a new patient whilst existing ones aren't getting what they need. Until that gets unblocked I'm in limbo; additionally BUPA do not cover any ADHD costs (except the diagnosis) - after that you're on your own and you either need to self-fund or go via the NHS; the NHS won't "just" prescibe; for me they want that to come from the psychiatrist and they'll then pick up the medication part of it - but see above about BUPA not funding ADHD costs.
If you go NHS all the way then you'll be on long waiting lists and, presumably, some sort of post-code lottery as to your experience.
I'm willing to self-fund to get to the point where the NHS will take over (and apparently that's a dice-roll too; my GP says he will prescribe once the shrink gets me on a stable dose, but not before - apparently some GPs refuse and require that you go via the NHS for everything, so you're on long waiting lists again); but am currently unable to progress due to the shortage of medication, as mentioned. I am also expecting relatively large bills as I will need to self fund both the psychiatrist and the initial medication prior to the NHS picking it up.
Anecdotally (reading ADHD forums on reddit) experiences in the US sound much more random.