I don't really remember how long it took me. I think maybe a little less than a month, but a girl at my gym got her grips about 2 weeks ago and i think they are broken in, but i am not sure. It may depend on the type of grips, but i don't know! Someone told me that to speed up the breaking in process, you can wear your grips around the house (i guess to get used to the feel of them). I also tryed to get them into the shape they would be on the bar and bend them like that (but i don't know if you are supposed to do that, it is just what i did.) And there is a certain way to fold your grips for storage so that the bend in the right shape, but i cant describe it
I'm going to assume dowels, but some of this can be used for palm guards too.
The quality of leather is a lot better than in my days, so it may be a bit different then from now. Some of it depends on the type of leather your grip is made from. Hot Shot are a softer leather, easier to break in. Grips like Reisport, my fav, are sturdier leather. The more you can AGGRESSIVELY do taps (either swinging or tap-hollows) with your grips on the faster they conform to the fold of the dowel. I am a believer in water, but it is true that water will also cause your leather degrade just a bit faster needing new grips due to stretch a bit sooner. I don't feel it's a huge significant difference, but that is my opinion from my experience. I feel the more aggressive you swing bars, the more likely you're going to go through your grips anyways.
Here are some tips I used in the days...
If the finger holes are too small out of the package I would slip the finger hole I need to stretch onto the "pull pin" that you adjust the low bar with. You have the turn buckle that turns, and the pin you pull. Sometimes beams have the pull pin too, unless you're using Speith equip. Gently pull and twist some, a little at a time, until you have the holes to their desired size.
After your first break in session, I encourage at first chalking your grip up liberally, using water to cake the chalk on, then folding the grip where your fold needs to be, stick it under something with weight, like a mat, and leave it over night to dry and mold to the fold it needs. The chalk should be an ever so slightly damp cake, not a goopy wet mess. This should help with the grip wanting to pop to straight as you release and regrab the bar. You only need to do it once.
If you are gianting, the quicker you can get to gianting with the grips on, the quicker the fold will mold to your hand. It's the kipping, pirouetteing, changes in hand placements and transfers that are hard to do in new grips.
I absolutely loved to do giants in new grips since I was a very aggressive tapper on my giants. I had teammates that liked me to start out the break in process of their grips so it was easier for them finish the break in.
As for grip storage, if you can close the wrist enclosure (velcro/buckle) then pull the grip around the wrist enclosure and tuck it into the middle of the enclosure to get the dowel to tuck in there, so it makes a ball. That's how I store grips. I've also seen people fold the grip kind of in an S, following the natural folds and then tuck them up in the wrist enclosure as well.