Scrolls are a secondary resource rewarded for leveling and Persian Position quests completion. Needless to say they are quite limited in number so spend them wisely. Though, do note you never lose Scrolls and if you mess up on your Academy tree, you have the option to spend drachmas to fix it (first time is free).
Spending Drachmas is done through the Academy. Simply open the Academy and allocate your Scrolls one at a time to available and open study improvements. There are several types of improvements: Most of the improvements are for Troop Movement Speed Boosts and Troop Production Speed Boosts. Additionally there are studies for decreasing tower repair time, reducing agreement update completion time (2), increasing available hero slots, grain consumption reduction, increasing the amount of Colonies, reducing veterancy cost (not implemented yet!), and increasing the amount of combat experience received in battle. Every basic unit in the game has corresponding Movement and Speed boosts which are unlocked in similar succession to their agreement sequence. You must unlock each tier group with a few Scrolls as well. By far the most important improvement (because it's the only one that can actual boost the strength of your army and over come grain production shortages) is the grain consumption reduction improvement. You will however have to make your way through a series of movement speed boosts before you get to grain consumption reduction. It is however well worth the effort to get there.