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Make sure you understand the basics of the new domain extremely well. You don't need to know everything in depth, but every piece you do know needs to fit together in your mind.

Ask questions until you think you understand, then have someone confirm your understanding. Those with experience in the domain will be able to recognize the right questions being asked.

In my experience, most seniors in a company are willing to help you get up to speed if they see that you're actually trying to understand the domain as opposed to just learning enough to get by.

Even though it seems like everyone else has a good understanding of things, this is usually not the case. Often people have bits and pieces of domain knowledge, but not a thorough understanding. These are not the ones who can really help you.

Find someone who has a good understanding that you seem to get along with. Be proactive and ask them if you could pick their brain over a long off-site lunch and then ask a lot of questions.