How long does it take for medication to kick in ?

It depends on many factors not least of which is the drug taken.

It depends on many different things.

What kind of medication, the dosage, the individual taking the medication, the method of how the medication is dispursed (eg. type of tablet, inhaler, injection, insertion etc)

Where's the medication taking effect?  An anti-gas medicine that you ingest really could take effect in seconds -- as soon as it gets to your stomach.  An ingestible anti-inflammatory that you are taking to counteract a pain in your back or joints might start to work in 15 minutes.  Doctors' instructions notwithstanding, an ingestible antibiotic can sometimes start having an effect within hours, or it might take several doses over a period of several days to notice any improvement.

Depends on the person and the medication.  It can be very quick or take up to an hour.

depends on the drug and how it is administered.

for example: Ibuprofen takes 20 to 30 minutes to work if you take it by mouth. It takes 1 to 2 days to work if you put it on your skin.

another example: When taken by mouth, you'll likely start feeling the effects of morphine within 30 to 60 minutes. According to the product label, morphine reaches peak concentrations in the bloodstream in roughly 60 minutes after you take it orally.

injected, it has an immediate effect.

Depends on the dosage