The Broomstick How-To - Left-Handed...

Five loops (top), and three loops.  See the difference?

Broomstick crochet has many uses - as well as scarves, shawls, bags and blankets, it can form a panel in the middle of a project, or one row alone could be used as a bracelet. 

OK... here's how.
Chain your required number, plus one.  How many do you need?  First, decide how many loops are going in each group.  Three, four or five is the usual, but there's nothing to stop you doing any other number, as long as it works for you and the look you want.
Say we are going to go for three loops.  I would want a multiple of three, plus one.  The 'one' is for the first DC (US SC).  I have worked 16 ch here - which means, if I want to, I can do five in each loop,

Turn, and work back in DC.  You should have fifteen sts.

Pull up the loop, and slide it onto your 'broomstick'.  In this case, it is a circular needle - just 'cos it's portable.

There it is.  Needs to slide a bit further on to the needle.

Put your hook into the next stitch, and bring up another loop.

Pull...

Slide on to the needle...

...and again...

...all done.

I've grouped them into three, with my fingers, just sliding them along.

If you're feeling bold, you can take the needle out altogether for the next step... but if you're not confident yet, or may have to leave your work, then leave 'em on the needle.

Just slide the first three off.

Stick your hook through those loops, pinching them at the bottom so they don't end up uneven.

 Pull a loop through...

 ... like so, endeavouring to keep the loops tall and taut while you work - that way the first loop you pull through at the start of the row will not pull the other loops down

 You're making it into a DC.  See how the loops have now twisted sideways, slightly?

As we have three loops on the hook, we need to work three DC altogether in each group, so two more are in order.

There's our three.

Same with the next group.

 Three loops, three DC.

All the way to the end, and here's your loop pulled up ready to put on the needle.  Just remember to keep your count right.