Chains are fine. They will not hurt your tires but can hurt other stuff if they are loose or there is not enough clearance. If you are going to drive with them for any more than a couple of feet (ie. more than just getting unstuck), if you are not confident in getting them tight when you first put them on, put them on, drive about 20 feet, then re-tighten them and you should be good to go for while (ie. several km). Loose chains are bad.
Always put them on the back. The only time you should use them on the front is if you already have a set on the back and you are pretty desperate. You also have to take more care with them on the front because loose chains can snag the hydraulic brake line or other stuff like your fender where this is not so critical in the back. They also cause steering problems on the front, so should be use with great care on the front. Putting chains on the front is a good way to get a broken thumb. When one wheel grabs and if the other don't it can snap the steering wheel across, break your thumbs and cause you to loose control. Generally you will not need four chains unless something is really dire, like going off road in deep snow pulling a four place, in which case you would use great care.
Just two chains on the back wheels of a 4x4 adds an amazing amount of traction, is pretty easy to do, and is quite safe. Putting a set of chains on a 2x4 can give as much or more traction compared to a 4x4 with no chains to give you an idea how much they help.
Hint, bring some type MAT (ie. rug, carpet, door runner, roll up straw mat) with you to lay on to do up the inside chain. Even with your snowmobile gear on, this is an uppleasent place and a mat helps. Always do up the inside connector first, outside last.
Best place to buy good quality proper chains is a commercial distributor like gregs distributing or commercial solutions. They are hard to find in retail stores (ie. near impossible). Don't by the silly ones from crappy tire, they are terrible. Don't use the cable types, use only chains made from solid chain on trucks. A set of chains twisted around an axle will rune your month (your tires will be fine though). I don't even think NAPA carries chains for trucks. You must buy them in the right size to fit your tires.
I use heavy duty rubber cords to keep the chians tight...putting them on both the inside and outside of the tire keeps the chians firmly in place...and if by chance you break a chain the rubber cords quickly pull the chain inwards so you dont tear apart your truck....
Take your time putting them on right the first time will safe a lot of time and money in the long run...
Hey, I just read this again, I see it's in the mud pit (sorry, I saw in in "new posts" and though you were talking about truck chains. I guess you are looking for chains on a quad, not a truck? Probably some of the same wisdom applies but you would have to get them from a quad dealer. I still don't think they would hurt your tires and you would want to put them on the back.
Good day. Even though i do not run tire chains on my quad, i do have about 11 years experience running tire chains on a bed truck (rig moving). I personally would run chains on front and back if possible. This keeps you from putting all of the torque on one set of axles. As far as front or rear only, i would pick the axles that are less expensive to replace. Tire chains will do damage to tires if they are left loose so keep them tight and make sure there are no pieces of tire chain left loose enough to hit anything. I also used tarp straps on outside but switched to shortened tie down straps. Again this was on a very large truck, not a quad. Run the best quality chain you can find, it will be cheaper in the long run.