The Basics
Any crochet project starts with a simple knot. To create this knot, wrap the yarn loosely around your finger, then behind the loop you just created. Slide the crochet hook through the loop, underneath the thread behind the loop, and back up through the loop. Pull the thread to tighten the knot. Start a project by creating a chain. Wrap the yarn around the crochet hook, and use the hook to pull the yarn through the loop already on the crochet hook. Repeat this process to make a chain of the desired length as specified in your pattern. If the project says to turn the chain at the end of the row, create an additional chain, then turn the project around so you can work back across the row you just created. A project will specify whether you need this extra chain, known as the turning chain, and if you need to make more than one.
Single and Double Stitches
For the single stitch, start by inserting your crochet hook into the first chain on the row you just created. There should already be a loop of yarn around your crochet hook from the chain you created. Wrap the yarn around the hook again and pull this loop through the first loop. You should have two loops on your hook. Wrap the yarn around again and pull it through the two loops to leave one loop.
For a double stitch, wrap the yarn around the hook before inserting it into a chain. Wrap the yarn around again and pull through the first loop. Wrap the yarn and pull it through the next two loops. Wrap the yarn around for the last time and pull it through the final two loops.
Working in Rounds
For rounds, you'll need a small, plastic crochet marker. Once you've finished your first row, insert the plastic marker through the center of the last chain and leave it there. This shows you where the row ends so when you create your second row, you can stop at the marker and won't create too many stitches. Move the marker to the end of the next row when it is complete and repeat this for each row you finish.
Start creating a round by crocheting the number of chains specified by your pattern. Next, join the last chain you created with the first using a slip stitch. To create the slip stitch, slide the crochet hook into the first chain, wrap the yarn around once and pull it through both loops on the crochet hook. There are two ways to continue working your rounds. Either insert the hook into the center of the small circle you just made and single or double crochet using the center as if it were a giant chain, or you can single or double crochet into each individual chain. The pattern you are using will specify which is best for your project.