Also, if it is a side of photography that you are likely to do on a limited basis (like me), it may not be one of the things on the top of your photographic budget list.
So I can offer a few pointers that should help you without having the need to spend “too much”.
Firstly, I would advise you to read my “Portraiture Discussion”. Not for any particular reason of course, other than to put you in the portraiture picture, so to speak.
Once you have read up on the subject and you decide you would still like to have a crack at it, the following items are what I use and you will find them also useful for some of the other types of photography you do.
First and foremost, you really need a good sturdy tripod and a second, not so sturdy, that you can attach a flash unit to.
Speaking of which, you will also need an external flash unit. A TTL (Through-The-Lens) operated one for ease of use and one that also swivels in all directions, enabling you to bounce the flash, either off a ceiling or nearby wall.
Of course, your camera should have a “hot shoe” facility and you will also require a sync lead about 2 or 3 metres long, to go from your camera to the external flash unit. Also an adaptor fitting, which screws on to the top of the second tripod and has a “hot shoe” attachment for the fitting of the flash unit.
On the adaptor fitting there is also provision to fit a photographic umbrella, you can use a white or gold one to bounce light onto your subject, or a black one to provide shade, if out in the sun.
“Why do I need all this equipment?” Do I hear some of you ask? “Why can I not simply use my on-camera flash?”
The main problem with your on-camera flash, is that when used to take portrait shots, there is always a black shadow behind and/or to the side of your subjects created by the bright, direct light of the flash. It also has very limited range and if used too close, it will produce a washed-out look on faces and/or facial features - induces "red-eye". With a bounced flash however, from an external flash unit, the light is bounced from surface to surface, resulting in a softer, more even diffused, natural light with very limited or sometimes no shadow at all - and no "red-eye".
I also use a little "Slave" flash. This unit is automatically fired when the main flash goes off and is very useful for a bit of side light, for instance, when and where you need it.
As far as a backdrop goes, if you are shooting indoors, a plain white or neutral coloured wall with no distractions is great, but position your subject, about one metre out from it and take the shots about two metres back from your subject.
You may need to adjust the angle of your flash until you get it right, so don’t be expecting miracles on the first day.
Use the timer setting of your camera a take as few self portraits till you get a feel for it, or to get some practice in, use a friend or family member to be your sitter. That way you can also have a bit of fun while you’re learning.