The first time I made a jumper I looked up every new technique in the only knitting book I had: The Odhams Encyclopedia of Knitting. When it came time to increase I chose the "Over Type of Increase" because it was the only one described as "perfectly simple". Although the book did mention that is was used mainly in lace patterns there is not one mention of the fact that a yarn over (for that is what is described) produces a hole. Somewhat fortunately I was also unwittingly purling eastern and twisting those yarn overs when I purled back across them.
We'll talk about yarn overs and how you can make them more evenly sized when worked between different combinations of stitches another day. For now, a few other increase methods, most of which are also "perfectly simple". There are a multitude of tutorials available on how to work the stitches themselves and I've linked to some good ones below, but it's often helpful to look at not just how to work a stitch but at the appearance it will give on your work.
Paired increases worked on every other row
Paired increases worked on every row
Make ones - make one left (m1l), make one right (m1r), make one purl left (m1pl), make one purl right (m1pr). The strand between the stitch just worked and the next stitch is worked into so that it twists. The leg of that stitch on the right side can lean left or right.
I find that when worked with just one stitch between a mirrored pair that it looks a bit neater to work the increases leaning away from the centre stitch — so m1r, k1, m1l. As shown above this becomes much more pronounced when the increases are worked on every row.
On the wrong side twist the stitch in the same direction as you want it to be twisted on the right side.
Twisted yarn over - substitute for m1
Sometimes make ones, especially if they're worked right above one on the previous row, can get too tight as you pull the yarn up between the stitches. An alternative that produces a structurally identical result is to add the strand of yarn and twist it.
A twisted yarn over can be made by working a yarn over and then working into the back of it on the next row. That will twist to the left. For a right leaning version work the yarn over backwards and then work into the front of it.
Alternatively twist a loop of the working yarn and place it on the needle.
Knit front and back - kfb, pfb
Often taught to beginners (one's who aren't determined to learn on their own like I was!) and rejected because of the bump it creates. Those bumps, however, can make rather nice design lines, especially when worked in pairs.
No worrying about leaning in different directions but the crucial difference is that the first stitch made from the second of the initial stitches will be the centre stitch. So if a marker is placed you would work to 1 stitch before the marker then: kfb, slm, kfb. Doing that on subsquent rows will result in a column of bumps on either side of the stitch right after the marker.
Lifted Increases - LLI, RLI
Worked into the stitch below the one on the needle, this is probably the most invisible increase method in stockinette although it can sometimes produce a visible hole. One of my favourites for top down raglan style shaping because when worked without any stitches in between the two pulled up stitches look like one upside down centred stitch. Of course, when working top down that stitch will be right sides up on the garment — a detail that shouldn't matter but just looks right.
The major pitfall to avoid when working lifted increases is working them on every row. If you try it it will quickly become apparent that you're always increasing into the same stitch, pulling it further and further up the work!
A nice alternative is to work two increases on the right side and none on the wrong side. Increasing twice on the right side is mathematically the same as increasing once on both sides and can be worth trying in other situations too. You can see this in the photo above where two RLIs are followed by two LLIs.