I bought a home fertility test from first response and it says that it MUST be taken on day three of your period. But I don't have regular periods. Is there any way I can tell when day 3 of my cycle is?

First, here is some info from the First Response site about the test:

If your ovarian reserve (eggs) is low in quantity or quality, your pituitary will produce higher than normal FSH levels early in the cycle, trying to stimulate your ovaries to produce a mature egg. In other words, when your quantity or quality of eggs (fertility potential) is low, your FSH level may be high.
Therefore, knowing your FSH level on Day 3 of the menstrual cycle can be helpful in finding out if you are able to get pregnant.
FSH level assesses ovarian reserve, one of the leading single indicators of a woman’s fertility potential and now it is possible to gauge your fertility potential through a simple at-home test with over 95% accuracy.

Now,as you said, the test is supposed to be performed on day 3 of your period. The only way to have a day 3 of your cycle is to start your period. If your cycles aren't regular and you aren't having a period, this is a problem. The test isn't going to work for you unless you start.

You are concerned about your fertility, and a good rule of thumb is this - woman of any age who do not have menstrual periods or have irregular periods need to see their doctor.

Good luck!