Usually a few days. Differs for each company. I would make it clear to the recruiter that while you're very excited about their role, this is a big decision for you and you'd like to get the offer from the other company before deciding. Set the expectation that you'd like until that date or shortly after to respond.

Do not do this.

Unless you’re sure you’re the best candidate they’ve had by a large margin, you will always weaken your position by saying you’re waiting on the decision of another company. A good hiring manager will immediately pick up that you’re not excited about the company.

Negotiating salary is a more likely way to extend the discussion, if they aren’t keen on giving you time to consider. If they need an answer before the onsite with the other company, on the worst case you can just accept and set a start date further out. If you do get an offer you like elsewhere, you still have time to contact the company you accepted and say circumstances have changed, so you (regrettably) won’t be able to join them after all.