Yes, you can jump in a western saddle, but it isn't wise. The weight of the saddle is alot for the horse (it can do damage to their back) and you arn't able to get into a proper position to get over the jump in a blanced way.
START FROM THE GROUND! Dressage. If jumping is dressage with speed bumps, then do dressage. Get the basics down pat. Rythem, lengthening, shortening stides. Then work with ground poles and caveletti. Having the horse bring their back up and carrying themselves. Then you introduce the jumps. Starting with little 6 inchers, asking the horse not to step over them like the caveletti, but to actually pick up their feet and jump. Then you raise it slightly and slightly until the horse is comfortable jumping.
For the first day of jumping, you really won't be jumping. Ground pole work is just as important. I've been jumping for 7 years and my trainer still has us working over cavaletti and ground poles.
A good trainer would really be the best route to go if you've never jumped and your horse has never jumped. Do you ride english?
Well, I would read up in english riding and training. Practical Horsemen, Dressage Today, Horse Illistrated, books. I would still sugest getting some jumping lessons so YOU know what you're doing because it is SO different.
I've jumped in a western saddle out on the trail when there is no other option other than over. I put one hand over the saddle horn as I go so if you end up being jostled you won't have such a hard surface hitting you in the ribs/stomach.
I don't reccomend teaching a horse to jump in a Western saddle. That's the very reason I switched to English....that and I wanted to do eventing, which is obviously English. On the trails, hopping over the odd log or across a small bank is fine, but constant jumping in a Western saddle is not good for the horse's back.