There are many, many ways to cast on and bind off, each of which has a different intended purpose and “best use.” These links lead to my tutorials for each of these cast ons. You may have to use your browser's "Back" button to return to this page after reading it.
The main concern when learning to cast on or bind off is to not do it too tightly. You will know if it is too tight if the edge of your piece pulls in compared to the rest. The only way to fix this problem is to pull it out and do it again.
When casting on, especially when you are learning, leave more yarn than you think you need or your first row after casting on will be extremely tight and difficult to work. A good rule of thumb is that there should be a space about the width of a stitch between cast-on stitches on your needle.
Other options for loose cast ons
A trick some use is to cast on to a needle two or three sizes larger than your pattern calls for, then knitting onto the required size after that. Or you could cast on around two needles held together. I find that this leaves too much yarn in the cast-on edge and makes it all loosey-goosey. Find the option that works best for you.
Ready to Cast On
Making a Slip Knot
The first step for most cast ons is a slip knot.
Knit Cast On
I recommend using this cast on when you are first learning, as it uses the knit stitch to cast on and you can learn that at the same time.
Characteristics: Firm, non-stretchy, neat edge
Good for: Visible edges that need structure, such as dish cloths, decor items, or casting on a few stitches for garment shaping (at arm scyes or above a thumb gusset.)
Other useful cast-ons
Backward Loop Cast On
Easy to do, but makes a very firm edge that can easily become too tight or, in contrast, leave long loops of yarn between stitches once they have been worked.
Characteristics: Easy to do, can be difficult to get correct tension.
Good for: Casting on a few stitches above a thumb gusset or for other garment shaping.
Long Tail Cast On
This is slightly more complicated to learn than the previous cast ons, but has a very wide range of uses. For many knitters, this is their favourite all-around cast on.
Characteristics: Firm, moderately stretchy edge, moderately easy to learn, easy to get proper gauge and tension.
Good for: Any visible edge that requires only moderate stretch. Perfect to begin a gauge swatch.
Super-Stretchy Cast On
The stretchiest cast on.
Characteristics: Very stretchy, creates a neat edge on ribbing that stretches as far as the ribbing will allow.
Good for: Any k1, p1 ribbed cuff, such as on socks, mittens, or sweater hems.
Provisional Cast On
Used when you want to be able to create “live” stitches on your cast on edge after working the rest of the piece so you can pick them up and work in the other direction.