I don't know anything about veins, etc.
But what I have done is to play around a bit with fingers (men's fingers, not my own.) Lots of lube and very gentle fingering to get used to the sensation. And I've used toys on myself. There are special anal lubes that have some numbing stuff in them - not totally numbing but slightly. Anne Summers makes something that has, I don't know, peppermint extract or something, that is sort of soothing.
If you do try anal I suggest you try it with someone with a small cock who is calm and patient. It's not the length that matters as much as how wide, and the width of the head matters most to me. If a cock has a big, round plum of a head that's harder than a bullet-shaped cock that actually grows wider along the shaft.
An arsehole are like tardis: bigger on the inside. The sphincter muscle is what you need to concern yourself with. I googled a bunch and found a tip: when the cock is about to enter and is pressing in, bear down as if you are trying to, well, poo. Although it sounds counterintuitive, this will sort of "pop" the head in. Once the head is in, you're pretty much good to go. The more relaxed you are, the better it will go. If I rush things, I end up with a stinging pain that is no fun.
Frankly, I'm a bit rubbish at anal. Some women absolutely love it. I sort of like it/can tolerate it. Maybe someone who has learned to love it will be along and we can both learn from her.
Oh, yeah - and buy an anal douche bulb thingy. The basic red one on LoveHoney is great. Once you start douching you'll kind of get addicted to it and wonder how you ever managed to feel clean without it.