Lake Balaton has been the holiday playground of ordinary Hungarians for over a century, and most of the accommodation is in private houses and apartments rented by the owners, often through agencies. All along the road there are signs for "Tourist information" which are really agents for accommodation and tours, rather than the official tourist offices called Tourinform. Many visitors arrive without booking and can usually find rooms for around Euro 15 per person/night. Costs for a house with 3 bedrooms can run from about Euro300/week to over 1,000 luxury house right on lake shore.
It's worth to book the accommodation before arriving because in July and August most of the places are totally full and it is hard to find a free room.
High season for Hungarians is the school holidays, from mid-June to the end of August, but many people go home by St Stephen's Day 20 August. The whole place becomes very much quieter by mid-August, and you can easily find accommodation. On the downside, lakeside bars and restaurants also close for the season.