Yarn of your choice
Crochet hook appropriate for yarn (worsted weight yarn = about a G or H)
Large knitting needle (Sizes US 35 or 50 work best. I will also use a 15 in this tutorial)

Broomstick lace is made by clumping large loops of yarn together with crochet stitches. First, decide how many loops you want in each clump. (4 or 5 is a good number to start with.) My swatch will start with 4 clumps of 5 loops each on a US size 50 needle, so I will need 20 loops total. (You may choose to do your project with only one knitting needle size, but I chose to change mine around to demonstrate how it can be done.)

Second, get comfortable holding your needle & hook. I prefer to hold the knitting needle sticking out from under my right arm, some people find it easier to clamp it between their knees or simply lay it on a table or flat surface in their lap.

Chain 19 (your number, minus 1) and pull the loop on your hook up and over your knitting needle.

Insert your needle into the next chain stitch and pull another loop of yarn up and onto the knitting needle. Working into the bump on the back of the chain makes the prettiest edge, but for the sake of simplicity, it is okay to use one leg on the front of the chain.

When you reach the end of your chain, you should have 20 loops on the needle.

Starting with the first 5 stitches, insert your crochet hook as shown:

Loosely draw up your working yarn to the height of the loops and pull it through the opening. Then chain 1 to close the stitch. (This chain does not count as a stitch when counting, and is only necessary at the beginning of the row. The rest of the row is sc only)

Work across the row, making 1 sc for each loop in the clump. This row in progress has 2 clumps with 5 sc's each:

For row 2, I chose to shrink down to a US size 35 and change to 5 clumps with 4 loops each. Insert your needle into the sc stitches and begin picking up loops and placing them on the needle. Continue in the same manner, this time taking 4 loops at a time and making 4 sc stitches in each.

Row 3 is done on an even smaller needle. I used a US 15 and made 10 clumps of 2 loops each.

And here is a finished swatch: