With leather tack you need a good, oil based cleaner such as saddle soap or Murphy's Oil Soap.
Use only soft, clean cloths to rub the cleanser into the leather, making sure you get into every crevice. Don't forget the underside or inside of the leather, as all those areas need to be cleaned too. Depending on the cleaner, you may have to buff or rinse off any excess.
Once the leather is clean, use a leather conditioning product. I like neetsfoot oil, but others swear by Lexoil and Leather New.
For synthetic tack, you can rinse it off with a hose. For more stubborn stains, a soft sponge and some dishwashing liquid will take care of them. NO oil based cleaners on synthetic tack, or you'll ruin it.
Speed Racer is right. However, I do some real extensive tack cleaning, including scrubbing the rust off of everything which can take weeks!!! That's my least favorite part of tack cleaning. As for the leather cleaner, I love Murphy's Oil Soap, and I use lexoil for my conditioner...lovve it!!!
For nylon halters and other nylon tack, you can just throw those in the washing machine. As for their saddle pads and blankets, I take mine to the laundromat and use one of their commercial washers/dryers since the ones there are meant to wash heavy duty items unlike the ones at your home.
Let me tell you, it took me over 3hrs, TOTAL today to clean my aunts bridle that hasn't been cleaned since she got it (thats a LOOOONNNGGG time, like over 5 yrs). To get the rust off, you are going to have lots of fun with that one my dear haha. It took me all day (with breaks here and there) to get rust off of my curb chain, and it still looks like crap. Make sure you have a stiff wire brush with some good 'Tarnex' stuff or something meant to get rust and, other nasty crap off of metal. Your fingers will hurt, mine still do lol