Sorry for taking longer to respond regarding this question.
All Patrons that grant Additional Spells associated with them grant them in the same way. They are additional spells added to you known spells (besides the ones you already picked) for your level. It happens automatically when your character reaches said level. Just don't piss off your patron before you find yourself unable to cast anything
Sadly, as I just came to realize myself, Shamans are exactly like Warlocks regarding the number of spell slots they have to use per day (and how they recover spell slots works in the same manner, as Corvas mentioned above).