The first thing you do when you are ready to learn to crochet is to buy a hook and some yarn. Then you to have to get the yarn and hook to play well together. :-) Choosing your hook and yarn is an article in itself. To be brief, you should choose a medium size hook, perhaps an I or J, and light colored, smooth, worsted weight acrylic yarn for learning purposes. Wool is okay if you're not allergic to it.
There are several ways to start your project. Which method you use depends on the type of project you are making and to some degree your own personal preference.
The most common method of beginning a crochet project is to make a foundation chain. Another method which is gaining popularity these days is the chainless foundation which goes by several different names. In that method you make the stitches and the chains at the same time. Regardless of which you choose, you will need to first place your yarn on your hook. To do this, we normally use the slip knot. There are several ways to make a slip knot.
The Slip Knot
Here is a video demonstrating two common techniques for making a slip knot.
Note: I am right handed so these instructions are for the right handed person. I have a video at my YouTube channel demonstrating how to begin crocheting left handed. I hope to do more in the future.
There is also another method of beginning the foundation chain which does not technically use a slip knot. I have a video which demonstrates that method. This was my very first video. Thanks to my husband for helping with the video filming and editing. The video shows the method of wrapping the yarn around the hook, plus one chain stitch. No audio instructions, but there is some pretty music :-)
If you are going to be working in the round, you have a few options for starting your piece. (When I say "working in rounds," I am talking about starting with a circle or ring in the middle, with your piece growing outward, getting larger, until it is the size you need.) You could make a slip knot and short foundation chain, then join it into a ring with a slip stitch, or you could work your first stitches into the first chain. But, there’s also a method that doesn’t involve making a slip knot at all: The adjustable ring. It’s also known as the “magic ring.”
Here is a brief video demonstrating how to make the adjustable ring.