بسم الله الرحمان الرحيم
Do this:
Calculate the number of hours between Maghrib and Fajr. For example, right now in South Africa, Maghrib is at 5:26pm and Fajr is at 6:02am. That's approximately 12 1/2 hours. Make it a whole number, 12, and divide that into three: 12 / 3 = 4. The first four hours is the first third of the night, second four hours is the second third of the night, last four hours is the final third of the night. The Mustahabb (recommended) time for Tahajjud is the last third of the night. That is a time when Du`aa is especially accepted by Allaah Ta`aalaa. It is a Mubaarak (blessed) time. In South Africa, from 1:30am until before Fajr will be the last third of the night.
Do the same by you. Find out what time Maghrib comes in and what time Fajr comes in, calculate the number of hours, divide that by three and you'll know what is the last third. Perform Tahajjud in the last third.
For those not in the habit of performing Tahajjud, a very simple method is to simply get up 15-20 minutes before Fajr, and perform Tahajjud (Qiyaam-ul-Layl) at that time. If you are not used to performing Tahajjud every night, this is what you should do, In Shaa Allaah. May Allaah Ta`aalaa grant all of us the Tawfeeq (ability) to make `Amal upon this great Sunnah, and to have Istiqaamah (steadfastness) upon it, Aameen.
والله تعالى أعلم
والسلام