To cast a spell you need 'spell slots' - so in D&D 5e, you can learn a certain number of spells per day, of certain level like level 1, 2 3 etc. That will be something you see when you open your spellbook.
But these are just spells you can potentially cast that day - to actually cast them, you need a spell slot of the correct level. NOTE: you can cast a lower level spell using a higher level slot - that usually gives benefits, like more damage (or extra creatures you can target, with say, hold person).
You can see little blue squares on the tool bar which show how many slots you have left for the day. For some classes, a 'short rest' replenishes those slots. For clerics, wizards etc you need a 'full rest' or a potion that simulates that like a potion of angelic slumber.
Also, note that if you are not proficient in armor, and you put it on, you may no longer be able to cast spells - so check under 'armor proficiencies' on your character sheet what armor you can use,. Shadowheart can use light and medium armor by default.
You can look at the message box on bottom right (pop it out) and mouse over the rolls info to see what bonuses/penalties were applied. If you hold the mouse over your to hit/damage on your character weapons, you will see how the bonuses are computed (not always correct!)
For spells, if you need to roll an attack to use them - like ray of sickness - you will find the bonus applied to your dice roll (without an special modifiers) at the top of spell book, along with the spell DC (save target) that creatures need to roll to avoid/reduce affects of your spell. Note that there can be additional modifiers to these from temporary affects, and these are not always well indicated...
