New database and new query should be fairly obvious. Script database as... makes SQL Server automatically generate a SQL script for you. Create to, for instance, would write out a SQL script that creates the database with your current settings. That way if you wanted to create the same database on another server you can just run that SQL script rather than manually setting it back up again or copying the datafiles.
Under tasks we have various database tasks. Detach basically takes the entire database offline and unlocks the files. This can let you do things like copy or move the physical database files on the machine. Shrink attempts to shrink the size of the database by removing empty space. I doubt you'll need to worry about this option often. Back Up allows you to back up the database, important for a production site or if you're going to be doing things that might trash the database (like complex data/table manipulation). Restore lets you restore a backup. Generate Scripts launches the Script Wizard so you can create sql scripts for things like tables and users. I doubt you'll find yourself using this option often (or at all).
Under reports you'll find various types of reports you can run on your database. Mostly useless. The rest of the options should be fairly obvious. On the next page we'll explore the database branch.