What's the difference between ved and kender?

What's the difference between ved and kender? Both of which are the present tense forms of at vide and at kende meaning to know in English

Here you can read, in depth, the distinctions between the words ved and kender so you can feel confident that you're using them correctly. 

At vide 

Verb Conjugation: vid, at vide, ved, vidste, har/havde vidst

 
Knowledge
The simple answer is that at vide or ved is your knowledge: to have sure information about something, to have enough experience to know something is sure or true.  
 
Knowledge, sure information, experience
 
Det er vildt, hvor meget han ved om fodbold. 
It's crazy how much he knows about football.
Det er rart at vide, at hun har det godt.
It's nice to know she's doing well.  
To have an idea about what will happen or how someone will act
 
Jeg vidste at hun ville spise min kage.  
I knew she'd eat my cake.
Det er umuligt at vide, hvad hun laver.  
It's impossible to know what she's doing. 
Have knowledge about the existence of something
Sortkaffe er det bedste jeg ved. 
Black coffee is the best thing I know.
En kold øl på en varm sommerdag. Det er bare det bedste jeg ved. 
A cold beer on a hot summer day. It's just the best thing I know.
There are several other nuances and uses of the word vide, but these are arguably the most common

Kender

Verb Conjugation: kend, at kende, kender, kendte, har/havde kendt

So, whereas at vide refers greatly to the knowledge you have, at kende on the other hand refers mostly to what you are familiar with, that is, for example: places, people, books, movies, items, systems, etc.

To be familiar with, to know a person
Hvor godt kender du København?
How well do you know Copenhagen? 
 
Kender du ikke min far?
Don't you know my dad? 
Hun kender vejen. 
She knows the way.
To know a system and thus how to use it
 
Alle kender alfabetets bogstaver. 
Everyone knows the letters of the alphabet.
Jeg kender faktisk programmet rigtig godt. 
I actually know the program really well. 

To perceive something as identical as previously seen, i.e. a person, a person's personality, building, a design etc (genkende = recognize)
Hun sagde, at hun næsten ikke kunne kende dig.
She said that she almost couldn't recognize you.
Kan du ikke kende bygningen?
Don't you recognize the building?
To have/have had a sexual relationship
Han har kendt mange kvinder.
He's known/been with many women.