Hi Rianon,
I don't know anything about natural IVF I'm afraid, but I thought I'd share what I know about testing for ovulation. I do most methods: temperature charting, ovulation predictor kits (OPKs), cervical mucus (CM) monitoring, and cervix position (CP) monitoring. I have also just started using the Clear Blue Fertility Monitor but haven't used it enough to test its accuracy yet.
Temperature charting (BBT) is by far the best method of testing whether ovulation has occurred, but cannot tell youwhen ovulation is about to happen, just that it has. Using a digital thermometer, take your temperature as soon as you wake up - put it next to your bed as you need to move as little as possible to get an accurate reading. You will find that your temperature will drop on the day ovulation occurs and then rises and stays high throughout your luteal phase (LP). Since your temperature will naturally fluctuate it is possibly to have numerous 'dips' before you notice a rise - it is this rise that confirms ovulation. I would recommend the Fertility Friend website if you plan to chart your BBT - it's easy and free to set up and takes all the guesswork out of charting. I have the app on my iPhone and it is very easy to use.
OPKs can be relatively cheap depending on the type you use. I use strip tests available on the Internet and Clear Blue digital OPKs that present you with a

! OPKs measure LH, which rises typically 24-36 hours before ovulation. So when you get your smiley face or positive strip test it's time to BD! I use these from CD 10 since my cycles are so erratic, and don't stop using then until I know for sure I've ovulated. One thing to remember is that the strip tests aren't like HPTs, where the test line only shows if you are pregnant: with OPKs you will always have a test line as there is always LH to some degree in your system. You are looking for a test line that is darker than or the same as the control line.
CM is quite simple to chart and can be done at the same time as a CP or when you wipe after using the toilet. The CM you want is called EWCM and resembles egg whites. EWCM can be stretched far between your thumb and forefinger before breaking - this shouldn't be confused with semen, which may have the appearance of EWCM but does not stretch as far. From menses you would expect to be dry, then begin to experience sticky and creamy CM before you experience watery and EWCM - both of which are potentially fertile. If you visit the Fertility Friend website it is possible to download an excellent ebook that details all of this and is free.
I find CP the hardest method of charting ovulation, and as a rule it shouldn't be the only method you use. Also, some ladies don't feel comfortable doing it. It should be done at the same time each day, and you should note whether your cervix position is high, medium or low, and whether the texture is firm, medium or soft. A firm cervix feels like the tip of your nose; a soft cervix feels like your lip. When you're fertile your high, soft and open - a few days before your period is due you would expect it to be low, firm and closed. It can take a few months to become familiar with the different stages of your CP - I have been doing it for 8 months (only about 4 cycles!) and only now feel comfortable noting doing my CP. So, as I say, don't use this as your primary method. If you use Fertility Friend you will have the option of entering all this data in as well as your temperature.
I hope this helps you choose the best methods for you - good luck! X x x