I love doing routes with 3 people. Once you are efficient at it, those don't take much longer than going with 2 people, you have someone to talk to when the leader is taking forever, and you have an additional hand, if you need it (for taking pictures, dealing with rope tangle, keeping an eye out on the weather, another belayer if the leader gets in trouble...)
You specified half-ropes, which pretty much only leaves you with one option: You don't swap leads. You have a designated leader. The alternative is a big untying mess at the anchor with three people and two ropes. Absolutely not recommended, and unsafe in my opinion.
Here are some things to consider when you belay two people from a belay anchor: Make sure you have an appropriate belay device (ATC guide or reverso,) and you know how to use it in it's auto-locking mode. Practice belaying two ropes that are moving at different speeds, without taking your break hand off! This is important, even though the devices mentioned above are auto locking. If you are belaying from a ledge, I find it much more efficient to just stack each rope on it's own pile, and then have each climber re-stack their pile once they are safely attached to the anchor. If you are not on a ledge, you have three options:
- 1) stack both ropes as if you were belaying one second and are getting ready to lead the next pitch (your previous question). This is the least amount of hassle, but both climbers have to climb at the same speed, and each climber has to be aware of how much slack is building up.
- 2) Buy a rope hook, or use a sling clipped to your belay loop and one gear loop to stack one of the ropes, making coils (small to large), and use the rope with which you are tied to the anchor to do the same with the other rope. This is slow and complicated. You also have to be careful that the second and third are not getting twisted once they are at the anchor. This you just have to practice, I find it impossible to list everything to look out for (someone else might not?) Once both climbers are at the anchor, flip and give each their rope back.
- 3) Buy two rope bags that can be used as rope buckets and proceed as if you were on a ledge.
If you are using ropes that are also rated as single ropes you have one additional option: Either the second or the third can lead on one strand, belay the second up, who will be attached to two ropes (one of which is trailing), and finally belaying the third up. I have done this, and it is fine, but you asked for "the best way," which this is not. Not swapping leads and leading up on two ropes is more efficient, since you can belay both, the second and the third simultaneously, given you have an ATC guide or a reverso.
In case you were curious why you can't to the latter with two half-ropes: It would mean that one climber is leading on one half-rope, which is not what they are rated for, unless they definitively state so. I do have a rope that is rated as both, and there are even ropes that are rated as singe- half- and twin.
As a closing remark: I would suggest being really comfortable with the system of one leader and one second before you take a third, both with swapping leads and one leader leading every pitch. Rope management becomes exponentially more difficult with two ropes, and everything becomes just a little less neat and intuitive at the anchors. As a bonus, here are a couple of skills that you should know before you even attempt to do a multi-pitch climb: Rappel without a rappel device (on a munter hitch or a carabiner break), belay a second from the anchor with a munter hitch, joining two ropes with the appropriate knot, being able to defend why you chose that knot, know how to back up a rappel with a prussic loop and fireman's belay, know how to ascend a rope with two prussics and how to back up your ascend with backup knots, know how to build multidirectional SRENE anchors (I guess this one is an obvious one), know how to escape a belay... I would suggest taking a class, if you haven't done so.