Prep work for pullups

Lat pulldowns with enough resistance that you can only do 1-5 reps per set with 3+ minutes rest between sets.  Do 3-5 sets every other day.

thanks don,  I will start with this.  I'm sure it will take me a few sessions to get the weight right and hopefully in a month when I get a pullup bar I might be able to do ONE !

thanks for the reply.  I can do lat pulldowns and rows with our bowflex but don't have a gym membership right now to use the assist pullup machine.

You're welcome!

Here's why this was my recommendation - You said you can't even do one pullup right now.  Strength is how much force your muscles can create for one contraction.  Since you can't do one rep, focusing on strength is the shortest route to doing a pullup.  No offense to any of the other posters, but some of those suggestions, while they will increase strength, won't increase it as much as a workout structure focused on it, meaning they're not the quickest way to a full pullup.  A workout structure with multiple sets of 1-5 repetitions near maximal effort with long rests that allow nearly full recovery is a strength focused program, and will usually result in the greatest strength improvements.

As a side note, 6-11 repetitions with 1-1.5 minutes rest typically focuses on hypertrophy (size gains), and 12+ repetitions with :30 rest focuses on anaerobic endurance.  In all of these structures, there is a fair amount of "crossover", meaning that a program focused on strength will still result in some size and anaerobic endurance gains, just as a program with the goal of size gains will still increase strength and anaerobic endurance, but not as much as if the program design aligns better with the primary goal.

This is pretty spot on.  

I do bodyweight exercises exclusively now and I would suggest 'just hanging'.  Yeah, just see how long you can hang and try to increase that.  That will strengthen that whole region too to eventually prepare you for doing a pullup.  

You can also get a step stool and start in the 'up' position of the pullup (chin at bar), kick the stool out of the way and do a 'negative' on the decline - just try to lower yourself back down as slow as possible - do a few of these with a few minutes of rest between.  This will develop the functional strength needed real quick.

I will do all of that when I get the pullup bar, I just don't have one yet and wanted to know what I could do with what I have now until I get one.  Grip could be part of my problem as I do also have some arthritis in my hands and my grip is noticeably weaker the last couple years (as in having trouble opening jars), I'm hoping to improve that as well.

How do you do negative pushups?  Just lowering yourself slowly?  I'm doing pushups on stairs now (so at an angle but full pushups rather than from knees).

There are different techniques that can be used for progression.  The most basic is to say if you can do 3+ sets of 5 reps, then increase the weight next session and reduce the reps.  If you're stuck and not making gains, you can then incorporate things like negatives as mentioned above, or slow down the negative (eccentric contraction) to increase the training stress applied in the session.

For most people most of the time, they can see some really nice progress just through consistent training with straight forward rep and set structure.  (Does this sound similar to much of the advice regarding endurance training?    IME, it's usually not necessary to employ some of the more complex techniques for the average person just trying to get stronger.  Now, if we're talking about power lifters or body builders, that's another story, but I'd refer them to another trainer who specializes in those sports anyway.