I learned from the local uni's science library. It wasn't any more helpful than the internet, frighteningly. But no one was hurt, so here's what I know:
What kind of cath to use?
Foley, can be ordered with sperm shipment. teeny syringe, not the 5 ml type
How far in?
a speculum would help. A typical cervix is about a cm long, so don't aim or too much further than that. You'd rather do a great inter-cervical insem than scratch the interior of the uterus (at least, I guess that's the choice I'd make...)
other thing to worry about?
Vision is limited. That's why they use those stupid, unnecessary, painful flipping pully things (forgot the name) at the doc's office. Take your time and it should not hurt at all. Also, we once had a dr. do a terrible IUI in which he introduced air into the uterus, causing extreme cramping and vomiting and bleeding on the way home. None of this is normal! If you mess up so badly, look out for signs of infection and boost your immune system to no end for a few days afterward.
The bright side is that you can't do much worse at home than many trained obs are currently doing.
Timing with frozen sperm?
Later worked for me AND dp despite all evidence to the contrary. Successful cycles: me = 31 ICI and 35 hours after surge IUI (freaking out since I had to wait for the dr to open to go get my sperm -- I usually feel that I ovulate soon after surging).
DP = 15 and 30 hours dpo
can a plain Joe REALLY do this?
YES. Your doc is no more trained than this. I read their textbooks. The most concerning thing is not getting air into the uterus. Tap the syringe well.