Chicken buses from Guatemala City leave approximately every hour, from 6AM to 4PM, and cost only a few dollars US. However, the ride is long, and it can be quite uncomfortable if the bus gets crowded (which it almost certainly will).
Alternatively, you can take a bus to Los Encuentros, and change there. A bus from Los Encuentros to Sololá costs 2Q and from there you can take another to Panajachel, for 3.50Q
Many tourist agencies will arrange tourist buses transport to Panajachel. A minibus from Antigua to Panajachel is USD $12 per person each way, though some among the number of agents offering the service could charge USD $20-25.
Adrenalina diagonally across from the post office (oficina de correos) has a good reputation
