How many hooks did you buy? A lot of people will make their beginning chains on a hook one size larger than what the pattern calls for, and then switch to the smaller size when they start the pattern, to avoid that issue of the starting chain being too tight. That's why it's good to have the basic set of five or six sizes to start out with, so you can adapt as needed.
If you only have the one size, then just purposefully think about not pulling the chains too tight. Relax your hands, let the yarn flow through your fingers. Don't pull. It should work out all right.
Did your set include some sort of instruction book?
To make a row after the beginning chain: Chain whatever number you need, plus one, for a pattern in single crochet. Holding the work dropping from the chain, turn it clockwise (if you are right-handed). Always turn your work in the same direction every time you turn at the end of a row, so the twists will be the same throughout your work.
At this point you now have the chain dangling from the hook. You will see that each chain looks like a small oval loop with one strand under that loop. You have some choices as to where to put the hook, under two strands of yarn or under one, depending on how you want the finished item to look.
I find it easier, usually, to do the starting row by going under just one strand of yarn, because I find leaving two strands to make the edge of my work looks more finished. But you will see the standard instructions call for going under both strands. Experiment with both methods and you will see the difference.
Anyway - so you have the chain dangling. Take your hook and insert it under the top strand or strands of the second chain from the hook. Loop your yarn over the hook, which is now on the back side of the work. Pull through. You now have 2 loops on the hook. Wrap the yarn around the hook again and pull through the 2 loops. You have now made one single crochet (sc) and you again have one loop on the hook.
Keep going until the end of the row. Count your stitches at that point, make sure you stitched into every chain.
Then make a chain, turn, start over. This chain is called the "turning chain." (Duh....)There ya go!
For sc, the turning chain never counts as a stitch.
For anything higher than sc, usually the turning chain DOES count as the first stitch. In that case, you will notice that you have a post (vertical part of the stitch) and a loop immediately to the right of that, which is the worked part of the stitch. In sc, you start immediately with that loop, because the one turning chain is not counted as a stitch. In double crochet (dc) you do NOT work into that very first loop, because the turning chain counts as a stitch. You will work into the next available loop, in other words the one to the LEFT of the first post.
As you continue your work, remember to work into the turning chain when you come back to it on the next row. Because, again, it counts as a stitch.
The directions for whatever you're doing will tell you if the turning chain does or does not count as a stitch, and if it's a pattern other than the basic straight crocheting back and forth, will also say how many chains back from the hook you're supposed to start.
Let us know how it goes. Experiment a little bit with making some swatches about 6" high of of the basic stitches. (Sc, half-doubles, double). You will get used to the feel of the hook and how the tension will be more consistent when you relax your hands.