Check with your family and friends. Many times family and friends are able to assist. Offer to pay for your pet's expenses while they are being kept.
Some area vets offer boarding. Contact your vet to check their services and availability.
Ask at any organization or church you may belong. They may be able to assist or recommend a boarding facility.
Check with your pet's groomer. Sometimes groomers also have boarding facilities or can suggest a place your pet can stay.
Check online and research local pet boarding. Most boarding facilities allow and even encourage tours of their establishment so that you can see all of the features they offer and the space that your pet would be staying.