Converting a(nother) Needle Pattern

This is a question that comes up a lot on the various "knitting without needles" groups, whether you call the thing you're knitting on a Knifty Knitter, a knitting board, a knitting ring, knitting rake, knitting loom, or some other name that didn't spring to mind just now.

How do you convert "X" in needle knitting to the knitting loom?

Here is one from BH-CraftJunkie that I was just answering on the KWON Ravelry group:

How would I convert K1, yo, K2, sl 1, K2tog, psso, K2, yo;rep from * to last 2 sts, K2 to my knitting loom?

Let’s just deal with this section: "yo, K2, sl, 1,K2tog, psso, K2, yo"

This is a seven-stitch (seven peg) repeat.

The "slip 1, k2tog, psso" is all one thing. In KWON (knitting without needles), it means "move two other stitches onto another peg", so that peg ends up with a total of three loops on it.

Where do those other two loops come from?

Let’s number the loops from 1 to 7, left to right. Right in the middle, you want peg 4 to end up having three loops on it. So first, put loop 3 and loop 5 from either side onto peg 4.

(To make this even more like the needle-knitted version, pick up loop 4, move loop 5, put loop 4 back on peg 4, and put loop 3 on top of that.)

That gives you your "sl 1, k2tog, psso" - in needle knitting, a double decrease, or three stitches decreased to one stitch.

But this would give you empty pegs (yarnovers, YO) on pegs 3 and 5. You want them on pegs 1 and 7. So what you do is move loops over: move loop 2 onto peg 3, and loop 1 onto peg 2. On the other side, move loop 6 onto peg 5, and loop 7 onto peg 6. (It’s complicated to read, but it makes a lot of sense when you do it and see it.)

What you end up with looks like this:
O--A--O
(or really, more like this: O//A\\O)
O, an empty peg
- or / or \, a wrapped peg with a slanting loop
A, a peg with 3 loops on it

Now do a normal wrap. If the peg was empty, now it will have one wrap. If the peg was normal (one loop), it will have two loops on it, and you just lift over and make your normal stitch. The center peg should have 4 loops on it now (three, plus the new wrap): lift all three of the bottom loops over, leaving one. All of the pegs should end with a single loop, so you can wrap and knit the next row normally.

And congratulations – now you are doing lace knitting!