What should I look for in weather reports in order to pick a day for glider flying?
For thermal soaring, which is the majority of the time in the sport in North America, the best soaring days are usually the day or two or three after the passage of a cold front with high pressure behind it, where light to moderate winds are forecast.  You want relatively unstable air without any inversions, no mid to high level clouds, and low humidity but preferably enough to form cumulus clouds to mark the thermal tops (if the air is really dry you have no clouds at all and have to troll randomly looking for lift, or look for thermaling birds, or look for other gliders that have found lift). In other words, it's those clear sunny days after a high moves through, the temperature cools off, and you get those nice puffy widely separated cumulus clouds and light to moderate winds.

If a front ahead of high pressure has a strong pressure gradient behind it, it's likely that the winds the next day will be strong and this is bad because it tends to break up the thermals.  In that case I would plan to go the day or two after as the high moves in and the winds die off.

There are a lot of other factors, like the ground moisture content (wet ground sinks heat and inhibits thermal formation), but as a way to try to judge the best likelihood of good soaring conditions, the 2-3 days following passage of a cold front rule is the most reliable. 

If you're not much at interpreting weather maps and can only go by the public forecast, and have to pick a day in advance, try to pick one of the first days following the day with storms and a temperature drop in the forecast due to a cold front, where it shows sunny or "partly cloudy" (which will usually be be desirable convective cumulus) for a few days after, and avoid really windy days which if it happens is typically the first day after frontal passage.

Exceptions to this are desert areas which have sunshine and good convective conditions for thermals pretty much all the time, and places like Florida where during any kind of sunny weather there is always convection (there is a localized thunderstorm somewhere in the state just about every day in summer).