Not much in all likelihood. There's going to be a new PM, and that's the only thing that's certain. But there
There already are signals by senior Tories that a PM who would pursue a no-deal Brexit will get kicked out of office. And the EU has made it crystal clear that it's this deal, period -- and the UK isn't in a position to renegotiate. So assuming new snap elections don't occur it's going to be about whether a new PM will be able to (finally?) sell the current deal to Parliament and/or the public, or convince the nation as a whole that actually, Brexit isn't going to happen. Or just kick the can down the road.
If snap elections do occur it's really anyone's guess. FWIW mine would be that the UK would end up with an election entirely focused on Brexit and it would turn into a wholesale referendum (again). And I'd stick my neck out and suggest that either Article 50 would end up revoked in such a scenario, or the resulting Brexit deal would be so soft that it would make Brexiters even angrier.
Side note on the latter point: May's deal is the hardest possible Brexit deal based on the redlines she gave the EU and what the EU is willing to accept without putting itself in jeopardy. IMO there is just no way a new PM will get a better deal, and the EU has also made very clear that even in the event of a no-deal Brexit a prerequisite to even beginning to negotiate a future trade relationship is to accept what's in the Brexit deal -- including the controversial backstop.