You can choose to have your sleeping bag professionally cleaned or give it a go yourself. First thing to know, your sleeping bag shouldn't be dry cleaned as the solvents used will damage your bag.
If you choose professional cleaning you should look for a cleaner who specialises in cleaning bedding or quilts or go to outdoor gear specialists such as Remote Equipment Repairs or Venus Repairs Workshop. Washing your bag yourself isn't hard but it is important to follow these guidelines.