You should apply for the business license on the website of Economic dept. of the respective Emirate where you want to start a business. You can also approach the Economic dept. and fill the forms highlighting your specific activity/activities and get the initial approval. Then you should rent office/shop as per the requirement. Even you can rent a virtual office as well where you can pay less rent if you do not require a physical office.
If you want to establish your business on mainland companies of the Emirate then you should have a UAE citizen as your sponsor and local partner or service agent which depends on the activity and type of trade license you own. If it is a professional license you need a service agent and if it is a commercial or industrial license then you need a local partner whose shares will be 51%.
Once you get the trade license you can start your business.