@johnny1217
Any general advice for speed?
I'd TL;DR this if I could, but it can't be shortened any further.
Fluffy kitten is on point regarding time and practice, but even more so a development of routine. Pick a spot, go around in a circle, whether it's bathing, drying, or the haircut, and stick to it. Methodical repetition makes you faster. New groomers tend to jump from area to area at random, myself included when I first started, and what this tends to do is make you lose your spot, and question if it was already done. You end up going over the same areas multiple times. That being said, there is no right or wrong way of where you start or end, more importantly its' about doing the same motions on every haircut as closely as possible. Each pattern specific cut will have its' own routine you'll develop for them.
Another tip would be not to obsess over small details when the entire dog isn't finished yet. Scissor the leg, and move on to the next area. You can spend hours on the same leg because you STILL see something sticking out, and it's driving you nuts, but that can be deceiving if the rest of the body isn't done. Wait until the main scissor work is finished, then go back and fine tune. Also, Make sure your clipper is tuned up and in good working condition. Replace the parts if you know how to timely, or have it serviced every so often. If you your blades are dragging, and you know that blade is not dull, or it happens with every blade you try and use, its' probably the clipper. That will REALLY slow you down if its' not working properly. Test to see if blades or dull or clipper isn't working by borrowing someone else' clipper and use your blades with it.
Lastly, on another note, be forewarned, unless i'm interpreting "all the dogs" incorrectly, it sounds like all of fluffy's clients come in all at once at the beginning of the day, and are discharged as her haircuts are finished one by one. Not all shops do this. My shop is appointment based, and you don't have the option of picking and choosing which haircut you want to do first, they're done in order they came in, with a 2 to 2 1/2 hour window for each dog. (every shop is different, but fluffy and I's are the two main setups you'll come across with some variation). Your 9am could be a golden doodle and your 10am a maltese. There is no easy dog first where I work x.x If you don't have a bather with my kind of set up, and you're booked on the hour like I am, things get a little more hairy(figuratively and literally xD )(Note: I have 8 years haircut experience with 16 years in the industry itself)
Edit: Did not realize I was not replying directly to OP. I'm still waking up xD