How do i know the single tablet taken for four days of azithromycin is working to cure chlamydia?

Test of cure: the way to know if it worked is to return to your doctor in the time frame that was discussed with you to get tested for cure. You partner should have also been treated and any sexual encounters in the meantime should be with a condom. Usually you return in 1 month to retest if you are concerned otherwise this is not necessary. Usually all 4 pills are taken at once.

Retest later: That's atypical treatment for chlamydia. The usual and recommended Azithromycin dose is 1 gram in a single dose (4 tablets of 250 mg). Probably taking it Z-Pak style over 4-5 days would work, but it hasn't been studied. Either way, there's no way to know it has worked except to be re-tested later. OTOH, Azithromycin is highly reliable (95+% effective) and you can assume it will be effective.