You can do a variety of techniques. There are trade-offs between speed and safety. The following is what I would do to make a very safe anchor that a bunch of people are going to climb on. It requires four carabiners, at least two of which should be locking, plus a cordelette or static rope.
Ignore the chains and the rap ring -- especially the rap ring, which can be worn and which you don't want as a single point of failure. Put a locking carabiner directly through the hanger on each bolt. (If you don't have four lockers, it's OK to use non-lockers here, since they're going to be redundant.) Using a static rope or a cordelette, put a loop of cord through both locking carabiners so that when you pull the two strands down in a V shape, it extends the desired distance. (E.g., if the bolts are above a lip, you want to extend far enough so that the climbing rope won't rub on the lip.) The V should be long enough so that it doesn't amplify the forces on the bolts. (If the angle between the strands is greater than about 90 degrees, you'll be amplifying the force a lot.)
If people are only climbing a single route from this anchor, so that there is only a single well-defined direction of pull, then tie the two strands into a big knot such as a double-strand figure-eight on a bight. Put two locking carabiners through this knot, opposite and opposed.
If people will be climbing multiple routes on this anchor, with different directions of pull, then tie two limiting knots in the anchor, and put one locking biner through each strand. This setup is called an equalette. It allows the anchor to self-equalize for different directions of pull, while limiting extension if one side fails. Some people I know here in Southern California who do a lot of sport climbing will just pre-tie an equalette and use it all day on a series of sport climbs that have similar two-bolt anchors.
Before climbing on the anchor, evaluate its safety the same way you would with any anchor, using a checklist such as SRENE.
A good book on this topic is Climbing Anchors, by Long and Gaines. The techniques I described above are shown in ch. 10, with lots of photos. These techniques are similar to, but not identical to, the ones taught in the AMGA single-pitch instructor course.
What is the preferred way to do it? Putting the rope through two quickdraws or one locking carabiner?
You can evaluate these setups using the SRENE acronym.
The two-quickdraw setup is solid and redundant, and if one side fails it's likely to have little or no extension. However, it's not equalized at all.
Re a single locking biner, it depends on how you are thinking of attaching it to the bolts. But in any case, if it's a single biner, it's not redundant. For example, if someone forgets to lock it or if the rope rubs on it and causes it to unscrew, you have a single point of failure. The risk is low, but I don't see the point of not using two lockers.
A general rule of thumb in climbing is that one locking biner is the moral equivalent of two non-locking carabiners, opposite and opposed. So that isn't the issue here, per se.
