The Huntsville Grotto is very much concerned with promoting safe caving practices. This applies to both horizontal and vertical caving. To that end we have written a booklet, Information for New Cavers, that contains a lot of important information about caving safely. Here is good site for learning how to tie knots.
Additionally, we actively train people to be safe cavers.
We run scheduled horizontal training trips, which are targeted specifically to newcomers to caving. These are open to anyone with an interest in caving.
The Grotto’s with the Huntsville Cave Rescue Unit (HCRU) also conducts basic vertical orientation once or twice a year, depending on the demand. Send an email expressing your interest to Huntsville Grotto. If enough members are interested and instructors are available a orientation will be scheduled.