There are a variety of places to stay on the island, ranging from extremely basic backpacker accommodations costing only about $10 U.S. per night to clean/comfortable/air conditioned places for $30-50 U.S., to a few more upscale places which are still usually less than $100/night. Travelers reviews can be found easily online.
Cabanas Vientos del Norte
Vientos del Norte is a great place on the North End of Big Corn Island. Ike Siu is the owner, and he has 8 rooms about 50 feet from the ocean. His rooms range from $10 per person in a dorm style up to $50 oceanview with AC/Fridge/microwave, etc, although you may be charged extra for using a credit card or some of the amenities. Also has wireless internet for guests. Ike will do just about anything for his guests. You can use the kitchen. Free airport/boat pickup and dropoff. Food is available.
Paraiso Beach Hotel
Paraiso Beach Hotel is a well known Corn Island resort, able to accommodate 45 people in 15 rooms, all decorated in traditional Nicaraguan style. They are made to make you feel right at home. The cabanas are built 80 meters from the beach. Paraiso Beach Hotel has bathing, diving, fishing, waterskiing and snorkeling. Coral reefs are just minutes off shore surrounding the island 10 to 12 feet deep, visibility 80 to 100 feet. Has a restaurant - basic breakfast is great, and free with your stay. Has a computer with internet access for guest use.