Language is by far the most important door opener, so put in one hour of learning every day for at least a year.
Mingle to get out of your comfort zone: Go to after-work parties and flea markets, take public transit. Use hobbyist/ meet-up apps. Read/ watch the local news.
Don't expect to be invited, especially not to people's homes. People might also be uncomfortable being invited to your home. Meeting in a public place is almost always the better option, unless you've gotten to know someone really well.
Irony/ sarcasm don't translate very well between cultures.
Europe has some lousy weather, so get watertight coats and waterproof your shoes and backpacks.
Take it slow.
Also: Enjoy it! Europe is a fantastic little place at the crossroads between Asia and Africa and I would never want to leave.
UK inhabitant here. Is being invited to someone's house a casual thing in the US? I don't think I've ever been invited by someone who isn't a close friend.