Wanting to get around "no pets" policies really isn't the right reason for getting a service dog. Persons with disabilities get service dogs because they need help to live independent lives.
The legal requirements for having a service dog can be rigorous. The landlord can require proof of disability and proof the dog is trained as a service dog. In one court case, a judge even ruled that a landlord can require the tenant to submit to examination by a doctor of the landlord's choosing to determine disability.
Forcing a landlord to accept a dog in spite of a "no pets" rule can lead to hostile feelings between landlord and tenant. It can become very stressful knowing the landlord is constantly on the lookout for any excuse possible to terminate the residency. There may also be criminal penalties for making false claims. In some states this includes fines and/or jail time.
It is usually more prudent to persuade the landlord to accept the pet with a Pet resume or find pet-friendly housing.