Here's a list of CDL schools and company driving programs in the Hudson Valley / Mid Hudson region / Tri-state area / Southern New York counties of Ulster, Orange, Dutchess, Putnam, Rockland and Westchester.
Columbia, Greene and Sullivan counties don't have CDL schools so you will have to commute or find a warehouse that offers training.
There used to be a few more schools in the area but they have closed over the years and there are more schools north in Albany and south in NYC.
I'm unaware of any community colleges in the HV that offer CDL training, it's possible there used to be some but you can search their websites or call them up to confirm.
Atlantic Coast Driver Training - New Windsor NY
CDT (Commercial Driver Training) - Kingston NY
Dutchess School of Driving - Fishkill NY
Golden Crown CDL Driving School - White Plains NY
Heritage Auto School - New Rochelle NY
Kerry Professional Driving - Middletown NY
Nyack CDL & Training Center - Spring Valley NY
Putnam Professional School of Driving - Brewster NY
There are also companies that train drivers, accept drivers with no or low experience, or do a warehouse/dock/forklift-to-truck driver position but openings and timetables may vary. If you have previous warehouse/dock work/forklift experience that might help. Call them up to determine whether they will accept a recent CDL grad from school, train you themselves or have you start as a dock worker.
Local Company Training Programs
A Duie Pyle - Rock Tavern/Newburgh NY - driver training program
ABF Freight - Montgomery NY - driver training program
Blue Rhino/Ferrellgas - New Windsor NY - entry level/seasonal Class A positions
New Penn - Newburgh NY - dock to driver program
NFI - Newburgh/Middletown/Wurtsboro NY - driver training program
Old Dominion - Middletown NY - driver training program
R&L Carriers - Montgomery NY - dock to driver program
Saia - Montgomery NY - dock to driver program
XPO Logistics - Montgomery, NY - driver training program
YRC - Maybrook NY - driver training program
There are more of these terminals in the HV area. Most of the warehouses and truck terminals are located in the cities of Kingston, Poughkeepsie, Newburgh, Middletown, Fishkill, Brewster and more in Rockland and Westchester counties. Occasionally you might find a lone warehouse or facility in a smaller town, so look up any warehouses near you and ask if they know about any trucking companies and programs. UPS, Fedex, DHL & Amazon might have some programs/entry level positions too but those jobs can be rough.
Most if not all of these schools and companies use manual/standard transmission trucks for training and road tests. Some use 8 or 10 speeds, others use 6 speeds which may be easier depending on each person. If you struggle with the manual aspect with some brands/models/speeds of trucks you may need to try different trucks/schools to see what works for you in order to get past the test and drive other manual or automatic trucks when hired by a company.
Some of these schools and companies do Class A & B training, others only do Class B so you'll have to call up each one and get details on what you are looking for, how much it costs, how you can get financial assistance if needed, how the process works and all the steps involved, etc.
Check with your local county Department of Labor / Orange Works / Career Center to see what info they have that might help you.
You can get CDL study guides from your local DMV office for free or check your local public library to borrow the book or study in the library.
Some of the tests in the DMVs are still done on paper, others have the tests on computers only.
You can also go to a trucking school with a company anywhere in the country but you may have to relocate outside of your home city or state for some time. You can put your stuff in storage and get on the road with them for at least 1 year (sometimes less depending on the company) and come back to do regional or local work later on if that works for you, or you might find a new area to live in while being on the road.
Atlantic - Recommended, no school is perfect but their trucks are in good shape and have good instructors
Blue Rhino - Seasonal position gives experience but insufficient training & equipment, safety violations and tough delivery job
CDT - The 2018-2019 season was not good, apparently students would be sharing a truck instead of one-on-one instruction, the instructor was not professional, half the class left and later there was a job posting for a new instructor but it's possible the situation has improved since then
Dutchess - Heard some good things about this school, some instructors from other schools trained here
Kerry - 2016-2017 season and before was not good, the trucks were breaking down, had road test scheduling problems, instructors not focusing on teaching, etc
New Penn - Used to have their own terminal in Newburgh NY, now share space at YRC. May be short staffed and a rough work environment
YRC - Had trouble getting info here and am skeptical about the conditions
The rest I don't know much about, you'll have to read online reviews and ask around for details. You can always change schools if something doesn't work out - ask questions and read the fine print before signing anything.
As with anything your experience may differ and it becomes a part time job when looking for a good school, instructor, job, etc so get a notebook and keep notes every step of the way. Google maps is useful for researching places quickly.