The currently available urine pregnancy home tests are very accurate and reliable at detecting early pregnancy.
They test specifically for the beta subunit of HCG, so there are few false positives (years ago they were less specific and gave false positives with elevated thyroid stimulating hormone or LH - this does not happen now) and they detect very small amounts of HCG (most detect less than 25 IU of B-HCG).
The day of the missed period the HCG level is usually above 25 IU, so home pregnancy tests are usually positive even a few days before a missed period.
The sperm meets the egg after ovulation, but the embryo takes almost a week to travel down the fallopian tube to get to the uterus. Once the embryo implants into the uterus, HCG is secreted into the bloodstream.
Theoretically, the pregnancy test can be positive as early as ten days after ovulation. We don't recommend taking pregnancy tests this early in the average patient, because you will detect chemical pregnancies that are very early miscarraiges.