There are a number of quick keys (keyboard shortcuts or keyboard controls) that offer alternatives for mouse control of the Eve client. These can be found in the client's Configuration menu and can be re-assigned to suit a player's preference. CCP documentation for default controls can be found at The Evelopedia. A printable spreadsheet can be found here.
New players may find especially useful the commands for All Stop (Ctrl+Space) and Drones Return to Bay (Shift+R).