How to know if a human female is fertile (can give birth to child in future) without making her pregnant? Any signs, tests?
Of course. There's several fertility tests available to determine the quality and quantity of egg reserve, and whether or not the there are abnormalities in the uterus.
However, some of them are invasive procedures, and all of them should be performed by a professional. I doubt the layperson would know what they're looking at on an Ovarian Ultrasound.
If you're asking whether there's an "easy" way that doesn't involve a trip to a doctor - then I would say 'no.' Casual inspection would only reveal any abnormalities in the vagina and the opening of the cervix, and hormone tests are only partial indicators.
Then again, if a woman has reached physical adulthood and is under the age of 38 then the chances of being infertile (or have difficulty conceiving) are quite low - about 3% to 10%. Infertility is usually much more of a concern to women who wait until after the age of 35 to have children, as there is a definite biological window (the number of eggs the woman was born with) to consider that starts to close as a woman nears her 40's.
It's also important to note that trouble conceiving can stem from either partner, and there's about a 40%-50% chance in a couple trying to conceive the male has an 'issue' and the woman is perfectly healthy.
If you are talking potential for fertility. There are a few...
If you are talking about immediate fertility... While I would not rely on them for the purposes of birth control there are several observable physiological changes that correlate with ovulation and fertility. These include
If we are talking about anatomical cues that are proxy's for fertility, there are clues based on the concept of sexual selection.
Note that these cues can be deceptive. Fat tissue may be deposited in both locations to imitate the fertility cues. Source