If you have permissions to restore on the target database server then that is by far the best way to copy the database.
If you don't have permissions, then you'll want to connect to the source and target databases with Management Studio and Import the data from the source. If you have simple primary key only indices on your tables you can import by right clicking on the target database name, then select Tasks, then Import Data. A wizard will walk you through it.
You can practice by importing the data into a new database on your local machine first.
If you have more complex indices or functions, sprocs, and views, you'll want to create the new database first, before you import the data. Same procedure, but select Generate Scripts. The wizard will walk you through the necessary steps. Under script options you'll want to make sure you select True for Script Indexes.
Again you can practice by recreating and importing locally. Though if you create locally you'll need to give the database a new name.