You would clean it the same way you would clean any colored carpet. Get a good carpet steam cleaner and get some carpet pre-treatment spray. Spray down the real dirty spots. When you put the water into the machine, try to get it as hot as you can through your tap. This should steam everything up when cleaning carpet.
Vacuum the carpet thoroughly. Then you can rent a steam cleaner to remove the stubborn dirt deep in the carpet fibers. You can use carpet stain removers in spray foam dispensers to remove stubborn stains.
First of all, I would recommend vacuuming over the dirty area. If the dirt remains, then it's time to borrow or rent a steam cleaner. Steam cleaners will be able to give your carpet a nearly new appearance!
Your carpet is very nice colored one. You can clean your carpet with vacuum cleaner. If you can do the vacuum cleaning daily, your carpet will clean and bright for a long time