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To practice common stitches, make a slipknot and a foundation row with 10-20 loops.
Single crochet (SC)
Insert your hook in the next chain, yarn over and pull through the chain (you now have two loops on the hook). Yarn over and pull through both loops.
Half double crochet (HDC)
Yarn over, insert the hook in the next chain, yarn over and pull through all three loops on your hook.
Double crochet (DC)
Yarn over, insert the hook in the next chain, yarn over and pull through the first two loops on your hook, yarn over and pull through the remaining two loops on your hook.
Back loop single crochet (BLC)
Each loop looks like a 'v' letter if you look at it from above. The chain closest to you is called the front loop and the one farthest away is called the back loop. Insert the hook into the back loop (only) of the next chain, yarn over and pull through the loop (you now have two loops on the hook). Yarn over and pull through both loops.
Slip stitch
Insert the hook in the next stitch, pull up a loop and pull the same loop through the original one without yarning over.
Commonly used abbreviations:
YO: yarn over
SC: single crochet
HDC: half double crochet
DC: double crochet
BLC: back loop single crochet
SS: slip stitch
SC2TOG: single crochet two stitches together
I hope this short description of the crochet basics helps you get started. You can come back to it every time you read a pattern or when you feel stuck after taking a long pause from crocheting.
To practice the basic stitches mentioned here, check out my scarf of all stitches pattern also on my blog here or available as a kit including the yarn and hook on Etsy here.
Tip: Don't forget to use stitch markers to keep track of how many stitches you have in a row and for quick counting.