a) A step-by-step: You'll either pick something off the wall or out of a book (this is called Flash art), or if it's a custom design, you'll discuss with the artist what you are after. They will draw something up, you might discuss changes, give your okay and they will then make a stencil of it. You will move to the sterile area (depending on the placement, might be a stool, a table sort of like a massage table, or a recliner like at the dentist) where the tools will be laid out ready to go (gun, packaged needles, water spray, lubricant gel, opened pots of ink) and the artist will glove up. They will shave the spot and clean it, usually with alcohol. Then they will apply the stencil by pressing the paper on and peeling it away. A faint blue outline of the design will be left on the skin. You will check the placement, and if it's all good, you'll sit down and the tattoo begins. The artist will put a needle in the gun, dip it in the ink, rub a bit of lubricant gel in and begin the outline. The feeling is hard to describe, but best I can say is a burning, cutting feeling. It's not unbearable and it varies according to where it is (over bones I find the vibrating worse than the feeling of the tattoo itself). It will be done in short bursts - or longs bursts if there is a continuous or straight line to do - and in between the artist will wipe away ink and blood regularly, and sometimes spray water on and wipe as well. Once the outline is done, the needle is changed and shading/colour will begin - the feeling is a little different, more scratchy and irritating like scratching a sunburn, and the heat feeling increases. The action the artist uses will be more a circular motion than the line motions of the outline.
When it's complete, the artist will spray water and clean it off, you'll have a looksee in the mirror, then they will rub something like vaseline or a lanolin cream all over it, and sometimes cover it with a wrap, sometimes not. The feeling after that is an ongoing heat, just like sunburn, and sometimes some tenderness and often swelling/welting.
You usually only leave the wrapping on for an hour, so after that comes off most artists will advise you to have a shower as hot as you can stand, and clean the tattoo gently, pat it dry carefully with a very clean towel and, once completely dry, apply more of the cream/gel. You have to put this gel on three or four times a day in the healing period. The healing process goes from tender, to a little scabby/flaky, the flakes fall off over time and it's completely healed within about 10 days to two weeks. You are generally advised not to go swimming or sit in spas or saunas during this time, and to avoid sun exposure.
b) This varies a lot! The basics you'll see in most tattoo shops is a front desk, lots of flash art and portfolio photos on the walls and/or in books, a waiting area and then an actual tattooing area with the chairs and equipment, plus sterilising equipment that might or might not be in view. Often it will be a body piercing shop too but not always. If it is, there will usually be a display of body piercing jewellery.
c) Not long at all. Probably half an hour.
d) Hugely varies but most places will charge an hourly rate, and maybe have a minimum base rate. My best friend who is a tattooist (here in Australia) charges around $110 an hour.
Sorry for the long reply but I thought the detail might help!