Frequent trains from Budapest Déli and Budapest Keleti connect the capital with both shores of Lake Balaton. Intercity trains stop at main stations such as Siófok, Balatonföldvár and Fonyód. Slower trains stop at all stations. Allow around 1.5 hours for a journey to Siófok and about 4000HUF (approx €19) for the one way fare (First Class). There are discounts for families (33%) and students (50%). Pensioners go free on trains, if in possession of an EU national ID card or passport. You must still obtain a ticket if you are a pensioner. Note that MAV Hungarian Railways introduced a system of supplementary tickets which are payable on most express trains, however short your journey, and these should be bought before boarding the train too. Not all ticket windows at the main terminals accept credit cards so you should check the signs. Many ticket machines have English and German language options. Airconditioning is found only in InterCity carriages,located next to the locomotive, for which another supplement is payable. Timetables can be found at 
Heviz Balaton airport at Sármellék (SOB) at the south-west end of the lake is about 20 minutes drive from Keszthely and Balatonmáriafürdő. The airport is currently served by Lufthansa and Germania flying seasonal charter flights from Germany. There are no signs of any regular services.
Since the lake is shallow, summer storms can create very large waves, and people have drowned in most years. A system of warning beacons around the lake alerts bathers to expected strong winds and storms: 30 flashes/minute, colour white/yellow means winds 40-60 km/h, and you should move close to the shore. 60 flashes red/white means winds over 60 km/h. Time to get out quickly!
Buy local wine of course!
With a vast lake, fish is a good option: Fogas (Pike-perch or Zander) is a white fleshed fish with delicate flavour; Keszeg (bream) is good roasted whole, Ponty (Carp) and sometimes Harcsa (catfish) is the base for halászlé (spicy fish soup), and you'll also find sullo (young fogas) on the menu. Game is widely found in the Badacsony hills and the Nagyberek (near Balatonfenyves), so it's worth looking out for pheasant (Fácán) and venison (szarvas) on the menu.
One kind of local food is lángos, a bread-like pastry usually sold on beaches. It is offered with different toppings like cheese, sour cream, and ham, or often plain just with garlic-sauce on top. Another common "beach food" is cooked corn on the cob (főtt kukorica), grilled sausages (sült kolbász) and of course, ice cream (fagylalt, or more colloquially, fagyi).
The hills north from Balaton are know for their wine. The best you can do is going for a wine spotting tour.
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).
There isn't much infrastructure for backpackers wishing to stay in a hostel. However, there is one hostel in Révfülöp on Balaton's north shore. Hullám Hostel is a perfect place for visitors of all ages and budgets, with a relaxed atmosphere and easy access to the lake, the Balaton Highlands National Park, and wine regions. They organize bike tours of the Kál Basin and offer traditional music nights, authentic Hungarian dishes cooked outdoors, and a friendly Hungarian staff. 
It's worth to book accommodation at Balaton 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.