I'll go over one method of setting up a top-rope anchor for climbing outside, specifically the Quad Anchor. This is specifically for climbing outside when there is a pair of bolts which are accessible by walking up to the top of the climb.

Please note: This article is only to be used as reference. Make sure to consult an experienced climber or certified instructor before climbing outdoors. Remember, climbing is inherently a dangerous activity and always carries some risk.

Step 1: Equipment Required

For the quad anchor, you'll need:

Between 20-30 ft 7mm or thicker cordelette
4 x locking carabiners

For the rest of your setup, you'll need (at least)

One rope (at least 2x the length of your climb)
Two climbing harnesses
One pair of climbing shoes
One belay device with locking carabiner
One helmet (strongly recommended)

Step 2: SERENE a Principles

Now that that's over, I'll go through what we're going to be building. This is a Quad Anchor. Whenever building a top rope anchor, you should use the SERENE A mnemonic, which which helps assess some of the fundamental aspects of an anchor's safety:

Strong

Equalized

Redundant

Efficient

No Extension

Angle

Strong This uses 7mm nylon rope, which is then quadrupled up. The anchor is strong, as each strand has a strength of ~12kN.
Equalized The sliding part in the middle allows the rope to move left/right if possible. The anchor is equalized.

Redundant If any one piece fails in the anchor, there is a backup. The anchor is redundant. (If one bolt, one carabiner, or side of the rope breaks, the knots will catch the carabiner and the other bolt/carabiner/side of rope will support the climber's weight).

Efficient This can take some time to tie, but is very quick if pre-tied. This anchor can be heavier than other options, if weight is important due to length of approach, or when used for multi-pitch.

No Extension If one side fails, the stopper knot in the cord will catch it after only a short drop. This anchor has little extension.

Angle Force vectors point almost straight down on both bolts (avoiding the American Death Triangle!) This anchor has a good angle when used with sufficient cordage.

Every style has different pros/cons. If you're lead climbing, you might be just fine with opposite and opposed draws as your top anchor. I like to use my setup, the quad anchor, when setting up climbs with accessible top bolts and when climbing multiple times with less experienced climbers.

Step 3: Inspect Bolts

Make sure that the bolts aren't too rusty or spin too easily. If they are, either set up an anchor with a sling around a nearby tree, boulder, or rock fixture; or just don't climb. It's not worth your life for one climb, and make sure to trust your gut if something doesn't feel right.

Even if the bolts look good, make sure to give them a good tug after clipping your carabiners in! Make sure they feel rock solid.

Step 4: Putting It All Together

First, tie your cordelette into a single loop; use a double-fisherman's for this. (Here's a great video by REI on how to tie it [link]).

Make sure that the knots are tight and there's at least 10cm (~4 inches) of extra rope on extending from the knots on both ends.

Next, double it up twice so you have four strands. Bring the two ends together, find the low point, and grab it. Note: make sure your double fisherman's knot is out of the way of either end or the middle. Then, tie two overhand knots on either side of where your fist was grabbing the rope. (You may also use a figure-8 knot here if you have extra rope and want to untie the anchor more easily later.)

Clip two (locking) carabiners through three out of the four strands with gates opposite and opposed, and clip two more carabiners into each end, one for each loop (to go to your bolts).

When you're at the top of the climb, clip the midpoint of your rope to the two opposite and opposed 'biners in the center, then lock the gates. Then, very carefully clip the two carabiners at the ends of the anchors to the two bolts in the wall, and lock their gates. When you're ready, gather both ends of your rope, check that there is no one at the bottom of the climb, yell "ROPE!" and throw both ends down.

And that's it! Remember to climb safely, and always be aware and do your safety checks for both the climber and belayer.

Another thing: I strongly recommend practicing tying this before you go to set it up the day of. You can even pre-tie it beforehand if you want to.

Step 5:

If you're more of a visual/auditory learner, REI made a great video about the quad anchor here:

https://www.youtube.com/watch?v=9liByriQRag

It's worth repeating: always climb with an experienced climber if you haven't been climbing outside! Take a class at a local climbing gym or find a friend who has been before and knows their stuff! This is not a comprehensive guide and every time you climb, you need to inspect your equipment, use common sense, and make smart and informed decisions.

That said, make sure to have fun and climb on!