I have used many approaches over the years. If I had an arm day things would be set up differently and I also like to rotate tri-cep with bi-ceps. Many days I would probably super set both muscles and likely do 4 superset rotations (so 8 exercises in total). That could be a tri-cep pushdown supersetted with a cable bi-cep curl. Then a close grip bench supersetted with a seated barbell curl. Incline bench tri-cep extension supersetted with db hammer curls. Finished off with a super set of reverse curls then bar hangs. Something similar to that but constantly evolving and and just having fun with it.
Now I train push, pull legs so arms are separated. I was going to state no real thought goes into things but I suppose after experimenting with training for over 20 years and trying pretty much everything I don't really need to put a lot of thought into things. Although my arm training can be very on the spot so "no real thought goes into it" so there is no planned sequence or number of sets and reps in mind especially when doing giant sets. Guys sometimes get lost in the details and they should just train with no limitations. Often I am going from movement to movement and I notice some guy has just finished his set so I lift whatever weight he was lifting and go from there.
That being said most days I know all the movements I will be doing and a rough idea of how many working sets but I often go on feel so I add in drop sets or whatever method I make up on the spot. My chest/shoulders and back portion of my training days are more fixed. The arms portion often is and I usually go with something simple such as skull crushers and 1-2 pushdown variations. For bi-ceps usually some heavy seated barbell curls and db hammer curls and a quick pump set on a machine to finish.
Now on certain days I just go for it and I try to exhaust the muscle from a variety of angles and using different weights and well anything goes. I use as much rest as I need. That could be no rest at all (90% of the time) so just moving fast between stations but usually having the weight set up. Although for arms (especially bi-ceps) you are limited because of the actually function of the muscle itself. Yes you can do 100 different variations of curls but at the end of the day you are doing a very similar movement over and over and it's unneeded. So I can usually have my bi-cep training done in 5-15 mins and that includes a variety of bi-cep and wrist curls. It's definitely quality over quantity and exhausting the muscle fast and getting those effective reps without unnecessary volume.
Last time I trained tri-ceps I done a few standard sets then I just done a big giant set (unplanned) with no rest between any set and approx 7 different movements. I think I done cable pushdowns, overhead extensions, dips backwards using the assisted pull up machine, machine extensions, rope pushdowns and incline push ups. That was no rest and I was maxing out most of the machines. Although the previous tri-cep session was different because I supersetted heavy db extensions and close grip bench press and tried to do a 2nd rotation with no rest and it was a bit stupid because I barely managed 4 reps on the 2nd set of close grip bench. Obviously in that example you need a spotter because I struggled getting that last rep up. For machines anything can go and you can just go crazy and get many effective reps in during a very short time and the job is done.