Degošie Jāņi — Burning man Latvia
Hitchhiking works very well in Latvia, and you should have no problem getting a ride anywhere, although you might have to wait for a while in less-trafficked areas. It is also harder at night, since people might be suspicious. Wearing colorful, reflective clothes, having a flashlight or head-light on(good for road safety, as well) and a sign will make this less of an issue.
Paid transport in Latvia is quite cheap. For example, a train from Riga to Daugavpils(2nd largest city in the eastern part of Latvia) costs Ls 4.95, or 7 EUR for a distance of 225 km. See www.pv.lv for timetables and prices.
Buses are also inexpensive, and to many more places than trains, although there might be only 1 or 2 buses a day to the more remote areas. www.autoosta.lv for bus timetables/prices.
There are many "maršrutkas" - minibuses - making the rounds in the cities and sometimes also between them (Riga-Jurmala, Riga-Ķekava for hitchhiking south, etc.)
Finally, there is a rideshare website operating: Braucam Kopā, or Drive Together. http://braucamkopa.com/lv/
Try the "usual suspects" - CouchSurfing, BeWelcome, WarmShowers to get a host. In smaller towns and remote areas, finding a host will be difficult. In that case, it should be no problem to put up your tent almost anywhere.
If you want to put it up on some private land and aren't afraid of asking the owner of the property, here is a text you can use: "Labdien/labvakar, es/mēs esam no _____, drīkst uzlikt telti uz nakti uz Jūsu īpašuma?" - "Good day/good evening, I/we are from ____, may we put up a tent for the night on your property?"
If you can't remember or pronounce all of that, no problem, just copy it down on a piece of paper and show it to them.
"Paldies" is "thank you", "lūdzu" is "please", and "cheers" is "priekā!" - you don't need much more than that to get by.
If you're camping out on the beach, be aware that making a fire is prohibited... But it's only if you get caught, and the more wild/remote beaches of Latvia don't have anybody checking to see if anybody is making a fire. So use common sense and be careful, but don't worry too much about it.
In this autumn/fall season you can find lots of berries and mushrooms in the forests. Make sure you know what you're picking, though, because there are (like in many other places) poisonous mushrooms that look similar to edible ones.
Dumpster diving doesn't work so well here, try Rimi or Maxima dumpsters and the Central Market in Riga can also have things left over at the end of the day(16.00-17.00), but be wary of security guards, many of whom are former convicts and can be mean bastards, to the point of physically assaulting you.
You can catch free wi-fi near most cafes or in some designated public places like Vērmanes dārzs(in Riga). In general - the internet here is widely distributed and fast.