Here is a detailed answer...
You will need a BBT thermometer. They are different because they are more sensitive than other thermometers. As mitchnorm said, they are on Amazon and are fairly cheap.
As far as the actual act of taking your temp, there are some things you need to do. First of all, you need to decide if you will take it orally or vaginally. Either method is fine, but some people feel that vaginally is more stable. But, whichever you choose, you need to stick with it. Switching methods can change your results, especially if you do it mid-cycle. So, if you do choose to change methods, do it at the beginning of a new cycle.
Second, you need to temp at the exact same time every morning, no matter what. I set my alarm at like 6:00am to take my temp because it's earlier than I would normally ever get up (so I don't risk waking up before then and ruining my temp) and then I go back to bed and wake up at my normal time later on. Any time is fine in the morning just as long as its in the morning and it's a time where you can take your temp everyday without fail. Also, make sure it is a time where you will get atleast 3-4 hours of solid sleep.
Next, when you do take your temp you have to make sure that you dont get up or do anything until you've taken your temp first. You can't sit up, you can't drink water, and you definitely can't leave your bed. All of those things affect your temp. (So does taking it later)
Lastly, just mark it down.
Most of us here use fertilityfriend, but you can use whichever app or site that you like best.