How do German people greet each other?

Do they shake hands? Kiss on cheeks? Hug?

Any difference between men and women in greeting?

Greetings are formal. A quick, firm handshake is the traditional greeting. Shake hands when introduced to a male.
Titles are also important and denote respect. Use a person's title and their surname. You should say Herr or Frau and the person's title and their surname.

If a man is greeting or introduced to a woman, wait to see if she extends her hand first to shake hands.
If she does not, do not presume to offer yours.

If Germans meet their neighbors or people they know in the street, a casual "Guten Morgen or Guten Tag" is enough, if they know each other better, they will shake hands and again shake hand when they depart with "Auf Wiedersehen".
In Germany only Family kisses and hugs.
If Friends kiss and hug they merely absorbing foreign trends.

well it depends on how well the person knows the other. the women there hug and kiss there girlfriends cheeks.when it comes to men they might kiss the guys cheeks if he were to be dear to her.the men there defenitly dont hug or kiss each other,but then again it happens at times.if you were to come across a random male or female from germany they would most likely shake your hand follower by "guten tug! wie geht's ihnen" meaning "good day, how are you ?or "good day how are you doing"?" hope this helped.

depending on the relation shaking hands(very formal) kissing cheeks and hugging (close friends) kissing lips (very close friends) saying 'guten Tag(very formal)' or just 'hallo', in some areas local greetings like 'gruess gott' in bavaria 'moin,moin' or 'tach'in Berlin and Hamburg, actually no difference between men and women or between the ages

Girls:
If she and the other person know each other well, they will either hug or kiss each other on both cheeks. It doesn't matter if the person she meets is a guy or a girl.
If two girls are best friends they might even greet each other with a little peck on the mouth.

Guys:
Guys will kiss girls on the cheeks when greeting them if they know each other well or fairly well. If they meet for the first time, it's usually just a handshake.
When guys greet guys it's usually just a handshake too.
But, a lot of men of other nationalities (i.e. Italians, Turks, Yugoslavians, etc) will kiss their guy friends on the cheek.

When meeting someone in a formal setting it's always just a handshake.

To be quite honest, it does indeed depend on the age of the people, and how well they know each other. It has less to do with men greeting men and women greeting women...

For example, I have seen guys in their 30's reach out to shake hands but also exchange a hug... I have seen guys in their teens simply greet each other with a high-five exchange just like you would see between Zack Morris and AC Slater on "Saved By The Bell". I guess the girls do seem to be a bit more friendly with the kissing of cheeks, but sometimes they just say "Hallo" and go about their business. It truly depends on how well you know one another.

Simply put, just an exchange of greetings (spoken) with a hand-shake is "formal", for people you're not very close with and don't see on a regular basis. A hand-shake/hug combo is usually used for men who WERE close but haven't seen each other in a while. And kisses on the cheek are for very close friends and family memebers.

As far as men greeting women is concerned, it's pretty much the same, but there is more of a tendancy to kiss on the cheek. I'm not sure if this is a mans hopes at becoming closer to the female, or simply implying "I'm not thretaning, I'm just 'one of the girls'", but a man shaking a woman's hand is VERY formal. Most of the time, even during a first introduction, I have been kissed on the cheeks by men. I get hugged very rarely, and my hand is shaken only by older men (35+). I hope this helped.