Welcome to FlyerTalk kayleeking!

Summer will be a peak period for travel whatever you do, so prices will not be as low as you pick up for say February. If you have not done so already, you can get an idea of prices from Orbitz, Kayak, Travelocity, Expedia, Cheaptickets etc. You could familiarise yourself with http://matrix.itasoftware.com and while you cannot book tickets there you can find out what the cheapest fares out there might be and you can also play around with its added search functions (month-long, multiple airports etc.).

General advice would for cheapest possible fares include being flexible about dates; accepting slightly more inconvenient connections or routings (e.g. via WAW or HEL); perhaps considering whether there is value in getting a cheap transatlantic to a major European hub such as LHR, AMS or FRA and picking up a cheapo train or plane for there (sometimes an option, but in summer maybe less of a saving to be had). Those are some general pointers to get you started!