How did ash marry Juliet and kanon/critias?
That's a question with two funny answers!
If you're imagining your usual human wedding of any variety...
Well, it didn't happen that way!
He's wedded to them by becoming their mates through pokemon customs unknowingly in both cases, and finding out after the fact.
With Bayleef, or Juliet, it'll be a chapter I have Planned for The Road Less Traveled. Ash learns that he walks around with Bayleef's scent on him, which Tracey explains is a common Grass-type behavior; they impress it on a partner for long periods of time, informing other Pokémon that they're hitched. Aa far as she's concerned, it's forever!
Ash has a mini-freakout and overestimates what that means, but after a few conversations that ground him about it, he's pretty chill about it. Nothing's changed. He never would've given Bayleef up, anyway!
She's his first wedded, in a sense. Beat everyone to the punch.
Latias was a bit different; even she didn't know it happened!
Ash was on a pilgrimage to the Raizen Mountains to bring the Rainbow Wing to Ho-oh, during a pretty turbulent time in his life. Latias found him fairly early into his trek through Johto, and insisted on following, even as Ash tried to ward her off at first. She tricked him into a battle, "proving that he was worthy of accompanying her" on her own journey.
To make a long story short, Latias broke down Ash's emotional barriers during that adventure, and they finally cashed in on the lil' fairy tale romance they started when they first met. They fall properly in love.
After Ash returns from his quest, he introduces Lance to Latias, who looks at them together and just... knows. He congratulates them.
Well, they're wed, of course!
Dragons mate for life. It wasn't hard to tell, by their closeness, that they've known one another; call it a Dragon Master's intuition.
Without Latios around beyond their childhood, no one thought to tell Latias about this, either; assuming he'd even known at all. It doesn't bother her any, though; Ash is always who she would have picked.
And, granted that she already knew she wasn't walking into monogamy with Ash by the time they'd expressed their feelings, Ash didn't have any reservations either. Nothing really changed.
She's his Pokémon, er. Partner. Both. Of course he's staying with her!