Putting on tights is easy, well it is with a little practice!
But before you do so, make sure that your hands and feet have no rough skin or nails. The sheerer the hosiery you are putting on, the more important it is for your hands and feet to be smooth. Men are traditionally less careful about such things than women, though many of us are catching up. You should invest in a foot file to remove rough skin – the edges of the heels and around the tops of the nails are the worst places. They must be smooth and soft. Check the back of the heels too, while you are at it.
Cut your toenails short with a pair of toenail clippers. Cutting the nails square, supposedly to avoid ingrown nails, is not necessary. You cut your fingernails round, yes? When did you last get an ingrown fingernail? Cut the toenails round to the top of the nail sheath, and then smooth all the edges with a nail file. Go over the tops of your toes with the foot file to remove the hard skin at the top of the nail sheath. Remember that toenails can sharpen themselves and may need re-smoothing even before they need cutting. If you still have hard skin anywhere on your feet, use a moisturiser. Remember, you are protecting your investment in tights!

Make sure if possible that your hands are as smooth as your feet should be. You might have little choice about this, but if you work with your hands, use protective gloves, barrier creams etc at work as much as possible.
If after all you cannot make your hands smooth enough, or you are going to wear a very sheer pair of tights, you can cover your hands with a thin pair of gloves when putting on tights. Surgical gloves will do at a pinch, and if they are too clingy, put a little talc on them. Purpose made hosiery gloves are available. A pair of pop socks on your hands or the legs from an old pair of tights will also protect the tights as you put them on. (Thanks to my friend Sal for that tip.)
I nearly forgot: Please shave your legs!! Why?
If the tights are new it helps to pre-stretch them. Stretch them lengthways as far as you can by holding the waistband in one hand and both tights feet in the other. Widthways stretching can be done later while you are putting them on.
Most people find it easiest to sit for the first part of putting on tights. (I am in the minority of people who do the whole thing standing up.) Put on each leg separately as far as the knee. To do this put your thumbs inside a leg of the tights and the rest of your hand outside, work your two thumbs gently down the tube, making sure you do not twist the leg as you do so. In the end you will have your thumbs in the toe of the tights leg and the material all concertina'd up. (At this stage you can pre-stretch the tights widthways by gently pulling your hands apart.)
Now carefully put your toes between your thumbs, and very gently pull up the leg, letting the material out as you go. The secret is to stretch the material the right amount. When you have got as far as the knee, let go and do exactly the same with the other leg of the tights.
Now stand up! That is the tricky part, as you are more likely to fall over at this point than at any other. Now you have to get the fabric up to the top of your legs! Put one thumb into each leg, holding the gathered fabric with your fingers and bring your hands up slowly. As you do so, move your hands from side to side around the legs and let out the material as before. Do not panic if the tights do not go all the way up at this stage, particularly if they are new. Pull the panty part of the tights up as far as it will go over your lower body.
The chances of a perfect fit at this stage are small, but do not despair. Now help the material up your legs, one leg at a time. To do this, grip a leg gently with both hands near the ankle and slide your hands up the leg to the top. If your hands are bare, give them a bit more friction by moistening them with tap water. Alternatively, your surgical gloves will help. The water (or latex) will provide friction to help to pull the material up without tearing it. (I do not think proper hosiery gloves would work so well at this stage.) It is important at this stage to avoid gripping the fabric between finger and thumb and pulling. If the fit is still not good, flex your ankles and knees a bit, and then repeat.
Hopefully you will now be wearing a pair of tights that fit you well. Good luck – it gets easier with practice. Expect the odd disaster, especially in the early days. It is best to start with heavier denier tights before moving on to sheerer ones. It is only quite recently that I have felt confident in putting on 6 denier ultra sheers!
Here's my tip for rough hands: buy 'Neutrogena' Norwegian Formula
unscented/concentrated hand cream. This is available from any high-street
supermarket. I've tried many hand creams, but this one is the best. Applied
to your hands each night before retiring (and over several days) ensures
the eradication of dry/rough skin.
Thanks, Jamod, for explaining in more detail the method of adjusting the
fit of tights using the friction of damp hands. You are quite right that
your hands have to be smooth in order to do this – a good point that I had
missed.