Roping Up
You will need a rope, 9.4 - 10mm by 50 metres long is ideal for most alpine mountaineering situations. Thicker ropes are more durable when being dragged about on the ground all day but the weight will slow you down. If you are going to climb a technical route I would just use one of the half ropes (unless it was super skinny in which case I would use one doubled.)
There is usually no need to walk with 50m of rope strung out between you and the simplest method to shorten it is to 'take coils' around the body. The more people on the rope the shorter the distance can be between each person, though I wouldn't have any more than 5 people on one rope.
For two people you need 10 - 12m of rope between you and the easiest way to measure this is to find the middle of the rope then measure out 6 arm spans (more if your arms are short) in each direction and tie a small overhand knot in the rope as a marker. Then tie into the end of the rope as normal, (see tying in below). Then flick the rope up across the front of the body round the back of the neck and then under whichever arm is most comfortable, putting a slight twist in the rope as you do so. The coils should sit about half way between the waist and the armpit - too long and they will slip off your shoulder, too short and the coils will be restrictive and uncomfortable to carry.
To lock off the coils, so that you are not instantly hung the minute you fall down a hole, pull a bight of the live rope between your body and the centre of the coils, then tie a half hitch back round the live rope so capturing all the coils. Then clip this loop into the knot loop on your harness with a screwgate krab. (See our taking coils below)
If you fall into a crevasse you will then be suspended from a higher body attachment, with the coils acting as a chest harness preventing you from turning upside down, which can happen if carrying a heavy rucksack or you're knocked unconscious in the fall.
With a party of three, put the third person in the middle of the rope with a bowline-on-the-bight or a rethreaded overhand knot that has the loop at the end clipped back into the knot loop with a screw gate crab to finish it off. A short isolation loop for the middle person will make life more comfortable, with three on the rope you can reduce the spacing between each person.
The question of the middle person carrying coils always causes a lot of debate, in most situations I wouldn't bother unless I was carrying a heavy load. The coils can be taken from either or both ends of the rope. A couple of extra options are to clip a krab through your rucksack shoulder strap and clip the rope running to your partner through it, alternatively you could make a chest harness out of a sling and clip the rope through that.
The only other thing to consider is whether or not you travel with a prusik loop already attached to your rope this has pros and cons. The advantage is that if either of you fall in a hole part of your rescue system is already set up. The further advantage is that if your partner falls in the crevasse it is easier to hold the fall if the centre of the pull on you is lower. By using a French Prusik on the rope you can lower this pull point and then release the load slowly onto your main tie-in, Pic 2 Travelling with Prussic on the rope this allows you to eventually transfer the load onto an anchor.