I have read that passwords are usually stored in a salted hash form. The salt is also stored. When the server receives password from player it tries to hash it again and then compares it with stored hash. ... How do i send the password over the LAN / internet? Sending plain text isn't secure. What are the usual methods to send passwords? What are the usual methods to log in to games that require user name, password?
Yes about the salted hash. Never store the actual passwords, store a one-way hash of the password plus a salt. If you stored the password directly it would allow someone who steals the password file to have everyone's password, which is bad for hopefully obvious reasons. If you only stored the hash it may be possible for an attacker with the file to do some dictionary attacks and find passwords; adding a generated salt value unique to the account means even accounts with duplicate passwords will have different hashes, so extensive work is required for every password.
Security over a LAN is different than security over the public Internet. Between machines you can use a machine-level authentication such as Kerberos, which is the fundamental protocol behind Windows network authentication and domain security, as well as most unix-to-unix machine security.
Across the public Internet (or as an added layer within your network) it is typical to establish a secure connection with TLS, get the username and password (stored as a salted hash) over the secure connection, and then shift to a session key. The session key can then be stored in something the user doesn't normally care about, such as a request header or a cookie. The server can do various tasks like invalidating a session key periodically, sending a new session key invisibly to the user, such as modifying the value stored in a cookie. If the key or the cookie expires and the user isn't active at the time, they must log in again. TLS provides protection against replay attacks, so an attacker cannot mindlessly replay a logon attempt they didn't participate in. (They can still connect on their own and record their own credentials, or run a MitM attack and record the credentials.)
Session keys are sometimes tied to specific IP addresses as another protection, allowing the server to potentially detect issues like stolen session keys or replay attacks.