On normal days you have two options. Shared tourist shuttles depart Guatemala City at 11am and 2pm. Cost is under $30 per person, travel through Antigua, and then on to Panajachel.
The second option is a taxi or private shuttle. Cost is over $100 in total and travel is direct. On Christmas day you would expect to pay more for a private (at least as an act of kindness to the driver for working on a family holiday).
How do I contact this "shuttle" to Atitlan?
The share shuttles, as noted above, aren't direct and you have to fit their (limited) schedules which may be even more limited with your timing - be sure to reserve in advance. They can take 5+ hours thanks to the extra trip into and time in Antigua. If you can afford to hire a driver, do that. You get to pick the timing and the trip should take about 2.5 hours.
Here are 2 transportation providers I’ve been pleased with in Guatemala for share shuttles, private transfers, and flight arrangements:
Adrenalina Tours: http://www.adrenalinatours.com
Rainbow Travel: http://www.rainbowtravelcenter.com
Our favorite private driver, Alfredo Garcia, is bilingual, personable, prompt, and safe, and has nice vehicles: firstname.lastname@example.org