It depends on the area where you would like to rent it, the quality of the building, square meters... on many aspects actually. We have the largest advertising board of private persons called
ss.lv - there you may study prices, conditions, areas... but it's available only in Latvian & Russian. If you want more infos, I can give them to you.
Overall, the average price for a house, I think, starts from about 500 EUR / month. You can find something even for 300 EUR, but it will be far away from the capital and probably not in the best conditions. But by September, the prices may go down a bit. Good luck.