A solo 2v2 League boost means the booster logs in to your account and plays the league matches while you take a break, usually with a partner of their own choosing. It is the fastest option, because the booster can play whenever the league and the queue are at their best. It suits customers who want the level and its rewards before the league closes and do not have the evenings to play.
A duo boost is something 2v2 makes possible in a way the one-versus-one modes do not. You play every match yourself, from your own phone and your own account, and the booster joins you as your teammate. Nothing is shared, no code changes hands and you learn from a stronger player in every battle. It takes a little longer, because your schedules have to match, and when a season is built around playing with a friend, the duo option fits it naturally.
Before posting the request, note your current league level and choose your target, and check which league is running and when it ends. Say whether you want solo or duo, which deck you like playing and, for solo, that gems, gold and Wild Cards must not be spent without your agreement. For duo, add the evenings and hours when you can play, so that offers come from boosters who are free at the same time.
After you accept an offer, keep an eye on the chat for the first minutes: for solo, the booster needs the verification code to log in; for duo, you add each other as friends and agree on the first session. From then on the booster reports each level in the chat. When the target is reached, the booster marks the order as finished, you confirm the result and collect the league rewards before the season closes.