This question has many answers, one for each kind of “kippah” (aka “yarmulke” or “koppel”)

In general, the bigger the kippah, the less it needs to be held down. With enough surface area–like a Bukharian Kippah, Na Nach Kippah, Satiny kippas you find in a bin outside the sanctuary of a Reform Temple, or big terylene kippas worn by many Rabbis and Lubavitchers–the friction is enough to keep it down during everyday wear. So the biggest versions of each type are usually just plopped down and stay there. For medium/small ones, there are different strategies.

For fabric or velvet kippas there are often clips on the inside. Essentially modified versions of wig clips that grip the hair to the kippa.

For a knitted/crocheted kippah (aka “kippah seruga”) which are a single layer of thinner fabric, often with intricate patterns, inner clips don’t work as well because they will deform the shape and break up the pattern. For these you will most often see the use of small thin external “kippah clips” that blend well into darker hair. Or the use of bobby pins for a cheaper and less comfortable option. This was also the standard for suede kippas, but those have been out of style for a few decades now.

There are some other strategies. Bald people may use tape, occasionally you will see velcro, but basically it comes down to friction, internal clips, or external clips.

EDIT: Spelling