I too just finished my first batch. I'm a Mr. Beer guy, so I have the basics down, but this was quite a bit different.
It was an extract kit from NB - Dunkelweizen. I did it in my kitchen. I bought a big tub (capable of fitting kegs sideways) for sterilization, so put a few gallons of water in, a bit of Star San and then threw all my stuff in. I kept the tub in the middle of the kitchen so I could just toss stuff in and take stuff out as necessary.
My brew kettle is a 32oz aluminum pot from a turkey fryer kit. I was concerned about keeping a boil without the lid on, but I just wrapped a little aluminum foil around the base of the pot and it worked fine on the stove. Boiling for 60 minutes straight is a little weird for this noob - no long boiling required for the Mr. Beer kits.
I hydrated my dry yeast as per Mr. Palmer, and that seemed to work pretty well. For cooling, I used my brand new wort chiller and it worked like a champ. I think I got my wort from boiling to 75 degrees in 10-15 minutes. However, getting it down to 70 was tougher. I finally lost interest and pitched at about 72.
I'm not sure about the hydro reading I took just before pitching, but I'd say it was around 1.39. I guess this step isn't really necessary, since we just need to check that the readings stop changing after about 10 days, but I needed to practice.
My only goof was doing a final shake-up on my better bottle to aerate just before topping it off to 6 gallons. I didn't pay attention while filling and it foamed out the top pretty good. Hopefully I didn't lose too many yeasties.
All in all, a fun experience, and I'm looking forward to figuring out little tricks to make it go faster and easier.