Here are some basic steps to install a divider wall:
1. Determine the placement of your wall. Make sure to measure carefully!
2. Locate the wall studs on both sides. This is where your 2x4 floor plate will be installed.
3. Cut out the baseboard to make your new wall flush with the existing walls.
4. Attach your base plate to the floor.
5. Build your frame using 2x4s.
6. Install drywall on both sides of the frame.
7. Finish the drywall with tape and mud.
8. Sand and paint your new wall.

I hope this helps! Let me know if you have any other questions or if there's anything else I can help you with.