Basic Weave
You do not have to warp a triloom before starting.  You start out with the empty loom and a ball, cone, or skein of yarn.  You work with the single strand of yarn, pulling yarn as it is needed from the ball.  The weaving is started at an upper corner with the loom frame placed so that the long side is at the top and the right-angle corner is at the bottom. 


Tie a slip-knot in the end of the yarn.  Loop it over the upper right corner pin and draw it tight.

Now loop the yarn over the pin the far corner, all the way across the top of the loom.  Keep it fairly tight.   Go under that pin, around and down as shown in photo.   Loop around the first side pin and stretch the yarn back across the loom horizontally.  These two horizontal yarns are the first warps. 

The weaving will get tighter later after you get more wefts woven across these horizontal warps. If you make it too tight, the fabric will pull in when you take it off the loom and be smaller than the size of the loom, and may curl. It will be hard to do the last weaving in the center of the loom also, as the yarns will get so tight it will be hard to pull the final loops down with the hook. You will not be able to loosen the yarn after much weaving is completed, so it would be better to err on the loose side until experience shows you how tight to pull the yarn. I know I have to keep telling myself not to pull it as tight as I can.

Now the first actual weaving is done. Loop the yarn coming back across the loom below and around the first side pin and continue around the next top pin. Weave the yarn loop under the top warp and over the second warp. Note that the yarn loop is under the top warp and over the second warp on both sides of the loop. (Arrows). You can do this weaving with your fingers or use a hook to reach up through the warps and pull the loop down. A hook is much faster and more accurate in my opinion. The size of the hook depends on the yarn thickness.  A long afghan hook is a good tool for weaving.  This loop will be spread apart clear to the far side of the loom.

The left side of the loop is hooked around the next side pin on the left side.  Loop it around on the outside of the pin as it will be stretched across the loom horizontally.

The right side of the loop you wove through the two warps is run around the outside of the next lower side pin and straight up and around the next top pin working inward, as shown by the arrows.  Note that the yarn still has its over and under pattern created by pulling down  the first weaving loop before the loop was spread across the loom.  The yarn now is ready to be again woven over and under the horizontal warps in a loop and the process repeated.
 

This time a hook can be run up on the right side of the loom to grab a loop.  Make sure the over and under pattern is the opposite of the last vertical yarn. 

You will find that each time you weave the hook up through the warps, you start by going over the bottom warp.  This allows you to quickly start the over and under weaving with the hook, checking occasionally to see that you are on the right track.   If you finish at the top of the loom in the right sequence, chances are that the entire course was accurate.  
    Make sure that the loop that goes around each top pin is going back down on the opposite side of the top warp. In other words, it is making a loop around the top warp and the pin. The weaving can be taken off the loom when finished without chaining the edges. If you see a loop at the top going back down on the same side of the top warp, you have made a mistake. It is easy to undo and fix your mistakes if you find them early.
As you pull a loop down through the 3 warps, start to spread it back across the loom.  Loop it around the outside of the next side pin down on the right side.  Make sure you don't skip a pin or get the loop around two pins as it looks like I am about to do in this photo.  On the other side of the loom put the loop around the next lower side pin and the next inward top pin.  Take up the slack each time you place the yarn around a pin to keep the fabric taught.   The one loop woven down through the warps finishes a section of fabric on both sides.  The next loop pulled down would be on the other side, a repeat of the step in the third photo above.

As you weave, both upper corners are completed and the upper central space is filled with warp yarn from the top down.  Weaving is done by pulling a loop of yarn over and under the horizontal threads and then spreading the loop to both sides of the loom, completing the weaving from the right and left corners inward.  An extra long hook is useful.  On a large weaving, you will have to pull down your loop part way and re-weave the hook up through the warps to pull it down lower.  On the largest tri-loom weavings, you may have to use a long hook and weave it up through several times just to pull down the loop.

 The final loop is pulled down through the narrow remaining space between the finished fabric in the center of the loom. All the top and side pins are used now. The yarn can be cut now and pulled through, as only one strand is needed to finish the weaving. The loose end can be tied at the edge of the fabric or a loop tied even with the fabric edge for crocheting off. There is a pin in the very center bottom (if you weave point down) but some weavers prefer to have this pin removed to make it easier to reach through with a hook to pull down the last loop. The last loop is cut, leaving a tail, and the ball end of the yarn is pulled back out. The tail can be tied to the last horizontal warp and used as a fringe. The corner pin is not needed for this basic weave.

Yarn colors can be changed to create fabric patterns, as in this photo. There are several ways to finish edges, depending of the project you are making. A fringe can be attached, as for a shawl. Different casting-off methods, such a crochet, can be used. If the triangle weaving will be combined with others, such as to create square or a multiple square pattern; the finished weaving can be taken off the loom without casting-off stitches. The long side of the weaving is improved by chaining off all the loops with a crochet hook. This can be done after the weaving is popped off the loom. There are different methods of weaving and adding fringes if desired.

Changing yarns, changing colors

The reason you do not want the knot from splicing yarn at the top or long side of the weaving is that is the part of the fabric that will be around the neck if it is a shawl. Also you do not want the knot in the middle of the weaving as it will show. Therefore you should put the knot at one of the side pins. If you are running out of yarn, the splice will be done when you don't have enough left to do another complete loop. If you want to change colors, you will make the splice when you have done a desired width of weaving with the previous color.

You figure out approximately how much of the old length of yarn will be needed to reach down to the next side pin by stretching the old yarn down to the next side pin one the side below where the last complete loop was done; but not weaving it in yet. Leave enough excess past the knot for a fringe, if needed. Tie a loose temporary knot to the new length of yarn then weave down through the warps as usual. You will be pulling the knot down through. When the yarn is pulled down snug, the knot can be re- tied so it is exactly at outside of the side nail. Now when you pull the rest of the loop over to the next nails on the other side and the top it will be the new yarn. If you are making a color change it will be the new color. If you were making a fringe, the tails of the knot could be left at least long enough to be part of the fringe. If not, the yarn tails can we hand woven into the fabric.

This site may have better instructions on triloom weaving: http://taliesin.confabulation.com/~workstead/continuous.html

There are links on this website below to many resources and also triangle loom weaving groups.

Hideaway Homestead Triangle Looms: www.hideawayhomestead.com/trianglelooms.htm