PSI and new tyres....

I use a lever or levers to install too. Some wider tyres here using the 26, 24 and 20 inch rims don't require extra leverage during installation but the only 700*23 here that will install without mechanical assistance doesn't bead due to gap hence it's a non serviceable combination.

Without inflating the tube much, inflating the tube such that it gains shape tends to retain such in the concave of the tyre thus helping avoid pinching the bead. Once on, thumb pinching the circumference works the tube up into the tyre.

+1 for talc.

If you need levers to get your tyres on... there's a problem.

Levers are for getting tyres off (ymmv).

No but quality tyre levers aren't expensive. Local bike shop easy, always plenty there at about $5 a set of 3. My mate broke some thin ones not long ago, good 1s are worth having.

Anybody tried one of these? Looks like interesting kit. 

http://www.wiggle.co.uk/x-tools-tyre-seating-tool-black-one-size/

The Schwalbe levers are excellent for tough tyres, you can use them to force the bead in to the central trough as you get round to the last section, freeing up your elbows from that duty.
If you're not experienced at fitting road tyres make sure you start the second bead install opposite the valve and work equally around the rim. It should only start to get tough around the 11 o'clock - 1 o'clock position

I have DA rims, and use conti tyres. They are a total biatch to get on and off. I'm pretty damn experienced and a builder, so I don't have weak hands, but I can't get them onwithout levers. The trick is to put it on as far as you can with your hands, making sure the first side fo the tyre completely sits in the trough. Once there is about 150mm (^") left to go on I use  a lever, and starting from each end of the unsecured bit, I use the levers making sure not to pinch the tube and only lift the levers as far as 90 degrees to the wheel. Ease a bit on, and move along a little. Hand on heart I've never put a hole in the tube this way.

bit of talc on the rim and a decent tyre lever, I think Pedros are excellent, EKIP (available from Planet X) have a very thin 'hook' on them so works great to avoid nipping the tube.

Unless you're over 110kg there's absolutely no need to put in 120psi even on the rear never mind the front and that's for 22/23mm tyres.

Insert tube into tyre, not inflated but not flat.
Put valve into rim.
Put valve thread on loosely.
Put 1 side of tyre on rim.
Push valve into rim and bead tyre there. Then pull valve back down and screw finger tight.
Work tyre onto rim.
When completely on rim massage entire circumference with thumbs while palms over tyres. Just in case there is a pinch.
When inflating visual tyre. They usually have a bead line. Check uniform fit.
I found that visual of uniform fit is a very good way to avoid pinch flats.

I run Vittoria 700c 23 tyres on my hybrid. I inflate to between 100 and 110 psi....because I always seem to get pinch punctures on the often crap road surfaces if I leave at about 80 - 90 psi. I usually inflate the tube until I meet resistance on the pump stroke, but that's just me.

What width is the rim? (the distance across the rim where the tyre sits). With a wide rim and a narrow tyre it's important to push the bead into the well of the rim. Contis in my experience always go on pretty easily. It's mostly technique and experience. If the tyres came folded I usually unfold them a couple of hours before trying to fit them and ideally leave them in the sun to warm up (obvs difficult this weekend!)

Crank Bros speedier lever, or go tubeless, or get more supple tires.

120psi though? Don't do that to yourself, it's not faster.

First of all, 120 psi is almost certainly nonsense. What do you weigh? I weigh 65 kg and run 25 mm tyres at 75 front, 80 rear. Fitting new tyres can ne a real challenge. Make sure you push the bead to wards the centere of the rim so they sit in the slight trough in the middle. You may still need to use levers but the trick is to constantly poke your finger, or the tip of a tyre lever, into the gap between bead and rim to poke the inner tube away from the pinch point.