I have been increasing my gym time, I want to work on increasing my overall strength as well, can't do a pull up to save my life and it actually would have come in handing for my backstroke start at a meet this weekend. I also want to focus on excercise that will help prevent injury from overtraining in swimming.

I don't have an actual routine but I use dumbells and do things like squats, lunges, curls etc. I also really like the lat pull down machine and the vertical row machine and tricep pushdown. I love the leg press because it really works all your leg muscles, plus those glutes!

I did notice since doing squats and the leg press, I have more power on my push offs on my flipturns (or maybe it's my imagination), I still have a lot of work to do on that though...

Fishgutzy is right, it is useful to have a personal trainer help you to start out, and would like to use one but don't have the money right now and my schedule is pretty irregular. I was thinking of recruiting a younger swim teammate who knows his/her way around the weight room to help me out.

I do. I have for years but then got with a personal trainer almost a year ago and I think it increased my efficiency in the gym. I certainly see a difference I never did before. I still meet with him once a week and then work out on my own one or two other days at the gym plus my swimming. I'll echo what the others said about hiring one but if you can't afford it every week, then maybe just do it a few times or like aliciamariaq said, find somebody who knows something. Given your shoulder injuries, having good form on everything would really pay off.

Here is what my gym workout generally looks like. Some are on machines and some aren't:

Quick warm up - 3-4 minutes on the treadmill or elliptical
Romanian deadlifts or regular deadlifts (I just started the latter because I couldn't lift that weight before)
Leg press
Lat pulldowns
bent over rows
chest press
seated rows
bicep curls
tricep pulldowns
abs (planks or hanging curls)
various shoulder stuff (I'll say more about that below)
stretching

One of the things he talked me into doing was stretching every day. I also have a quick shoulder routine with very light weights that I do nearly every day. It is similar to those exercises that SwimmyD recently posted. I am not in your league in swimming and don't get the yardage in but I have been trying to stave off some niggling shoulder and neck problems and this seems to be helping.

All that said, I was NEVER able to accomplish all this when my kids still lived at home. There was always some other pull on my time so I did what I could.

One last note on pull ups. I have never been able to do them and never plan to. I am distinctly bottom heavy and can't imagine lifting all that weight with just my upper body. That would be unfair to my arms and shoulders.