It can always be a little hard to maintain the discipline required for practicing. If you are just practicing over and over again in your lounge room, with no one else around to provide you feedback, it is hard to know if you are making any improvement. With no encouragement or reassurance that you are making any progress, this can lead you to lose the motivation required to keep practicing.
Recording your efforts is a great way to overcome this and help spur you on to improve your playing. Taking a recording of yourself can give you confidence that in fact, you do sound pretty good, and that you should continue practicing so you can sound even better! It is a great way to reassure yourself that all your hard practice is in fact paying off.
Observing or listening to a recording of yourself also allows you to take an objective look at your playing style. This is something that is hard to do when you are caught up in the heat of the moment and knocking out a particularly personal, trippy rhythm.
Recording yourself allows you to see which of your playing skills sound best and have the best impact. It also allows you to observe aspects of your playing that you may want to iron out. Most importantly, recordings assist you in taking an objective look at yourself so you know where your weaknesses and strengths lie.
The information provided here is simply for those who are looking to record basic sound or video files, cheaply and efficiently, for the purpose of practicing. Far more advanced information information on home studio recording can be found elsewhere, and that topic extends beyond the scope of this web site.
Probably the easiest and cheapest way to start recording sound, if you don't have any recording equipment at all, is to record straight into your computer using the standard sound recorder program that generally comes pre-installed with your computer.
It can be found somewhere in the "All Programs > Accessories" folder (or similar) folder in your computer. You will need a computer microphone, or if you have a laptop, there should already be one built in. The sound recorder program will look similar to one below. Simply hit the record button and play!

Once you are done, save the file. If you can, give it a name that reflects the phonetic version of the rhythm you just played, for example "ee aw eeah aw". This might seem a strange naming convention, but it will be much easier to search for your practice rhythm on your computer this way if you want to revisit it later, than looking at a myriad of "practice rhythm (insert infinite number here)" files. Also, just looking at the list of files of phonetically spelled rhythms on your computer is useful in prompting you during practice sessions.
Play back the file in a media player such as Windows Media Player. Easy! It may not sound so great, and your computer microphone may have freaked out when you did the horn sound, but you still should be able to get a good, general idea of how your playing sounds.
If you want to improve the quality of your sound recording, you will have to start buying stuff. Cool!
There are audio interface devices that you connect to your computer via USB cable or Firewire port. These have XLR microphone inputs so you can record from a dynamic or condenser microphone straight into your computer. They come with software that allows you to make adjustments to the output, record sound onto your computer and make simple edits. Examples of this are the Line 6 Pod Studio (USB) and the Presonus Inspire 1394 (Firewire).
There are also minidisc and digital recorders that give you a more portable option for recording your didgeridoo playing. These allow you to record in any location, and then transfer the sound recording to you computer when you are done.
Various recording options for the home didgeridoo recording amateur: the Line 6 Pod Studio UX1, a Sony Minidisc recorder and a Tascam digital recorder.
With regards to microphones, either dynamic or condenser microphones can be used for recording didgeridoo. While condenser microphones are apparently most suitable to recording woodwind instruments, dynamic microphones seem to do the same job, as well as being cheaper, more durable and not requiring phantom power. If you are going to get a condenser microphone, make sure you have a phantom power source. If all this is going over your head, and you just want to record something, just grab the nearest microphone you can find.

A dynamic microphone on the left and a condenser microphone on the right. All of this can get quite confusing, but if you're a gadget buff, you may have never known playing didgeridoo could be so much fun!
Finally, once you have recorded some of your playing and it is sitting in files on your computer, you may want to do a little sound editing. Editing is handy if you want to cut unwanted silences at the beginning or end of your sound clip, if you want to cut out ugly bits, or even if you want to improve the sound quality of your file a little more or throw in some effects.
Probably the best, free sound editor available on the web is Audacity. Click on the link provided and download it for free, no strings attached. It has a pretty simple interface and allows for easy slicing and dicing of your sound file, as well as making minor tweaks and effects.
You don't really need to use any of its features for the purpose of playing back your recordings for practice, but it can be handy. For example, if you are sending your recordings to other people to get their feedback, it will make their lives easier if you edit out the bits where you are running back and forth between didgeridoo and mouse button.

A screen shot of the Audacity interface.
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Recording audio or video of yourself allows you to take an objective view of your playing skills in order to improve them.
If you have a computer, you can probably start recording and listening to yourself right away.
If you want to record sound using more than just your computer microphone, there are quite a few simple, inexpensive options.
Audacity is a great, free sound editor that you can use to edit your sound files and share with other people.