Quick answer
К к is the k of “kite”, unaspirated. As a word, к means “towards” and takes the dative.
Кк
Кк
k
ктоwho
How to say it
An English k with no breath after it. Hold a hand to your mouth: there should be no draught.
ктоwho
какhow
ко́шкаcat
кни́гаbook
рука́hand
кварти́раflat
К as a preposition
A single letter meaning “towards, to (a person)”, always with the dative: к врачу́ (to the doctor), к восьми́ часа́м (by eight o’clock), ко мне (to my place — note the extra о before м).
The spelling rule
After к, г, х Russian never writes ы, я or ю — only и, а, у. That is why it is кни́ги and not кни́гы, and why adjective endings look irregular after these letters: ру́сская, ру́сские.
Typical mistakes
Aspirating the к in как
no puff of air
Russian stops are unaspirated.
к мне
ко мне
The preposition grows an о before awkward clusters.
Check yourself
Which word contains К?
кто — who.