How can I find a Server Browser to play with my friends?
There's no server browser at the moment; you'll have to share your IP address with your friends to connect. There's a button at the top of the menu that says 'Hold to show IP', which will show your IP after you click the 'Play and Host' button, which you can give to your friends to connect with.
A server browser is planned, since you can't really safely share your IP with strangers, but I have no idea how long it'll take to make
That usually happens either when someone has a firewall blocking the game, or someone's ports are closed. Port Forwarding ('opening' your ports) depends heavily on your router, but you can find useful guides for port forwarding most (if not all) routers at portforward.com/
Firewalls will usually pop up with a warning when the game starts asking if you want to let it connect to the net. If it doesn't, you'll have to manually add it to the 'allowed' list.
I'll try to add some ways to bypass the port problem, since port forwarding is a bit of a hassle, but I don't know how long that'll take.