A handshake is a common face to face greeting in much of the world. A poor handshake (like in this photo) will speak volumes.
Always use your right hand. Firmly grip the other person's palm and shake up and down a couple of times. Don't offer a wilted hand but don't grip the person so hard that you can see their face contort and hear their bones crunch.
The handshake ideally should be used with direct eye contact. A smile will also go a long way. The British are generally a non-tacile nation and so avoid complicating the handshake with a pat on the back or a double handshake.