What A Familiar Can Do
The sprite familiar can do anything a Sprite enemy/NPC can do acording to their stat block. If a familiar has something like Blind-sense (bat) or better perception than you, you can ask/tell it to look around for you.
The stats block only list bonuses that are proficient, other scores (like Arcana or Religion [+2]) would be determined by the typical way that is done for a player. The Monster Manual lists the mods after the stat, and you'll see they follow the same rules as players (+1 to modifier for every 2 points after over 10, -1 for every 2 points under 2). With the sprite, that means s/he could do a athletics check, but his/her modifier is -4. Yes, you're reading the stats right, are extra bonuses.
Strenght Save: -4
Dex Save: +4
Slight of Hand: +4
Con Save: 0
Int Save: +2
Wis Save: +1
Animal Handing: +1
Cha Save: 0
Passive Perception: 13
It can, even, perform the "help" action for you or a party member for any action the Sprite is able to do. It might even make sense to help your sprite look around (i.e. Advantage with the higher perception modification). Likewise it is terrible at lifting (athletics), but it can still "help" you lift providing you advantage with your strength.
The familiar can provide advantage on attacks to an enemy if he/she is within 5ft, and spends its action "helping" by distracting the enemy (which it can do while invisible) or by flanking rules (which it has to be visible to do).
The familiar can also be dismissed and brought back in a different form (bat, cat, etc.) following the rules in the Find Familiar Spell.
The familiar can, of course, deliver touch spells cast by the Warlock.
What A Familiar Can't Do
The stat block doesn't list any tool proficiency, so the sprite can't pick locks or like. Which means that it can't provide "help" for those tasks either.
As a Warlock, your sprite can attack but at the cost of an action, but unless you can't act for some reason, an Eldritch Blast or other spell is going to be more effective.