This statement made a little bit nervous and I wanted to know what should be expected especially in the first few weeks? Does the PI or anyone else available in the lab demonstrate the techniques that will be needed for later and then allow you to work independently or does it vary each day?
Yes, a current grad student or postdoc should look after you for the first few days to make sure you are not dangerous and teach you basic techniques. Once they are happy with you they will stop looking over your shoulder all the time and just wander over and have a look now and then. Eventually you'll be left to you own devices unless you ask for help.
You are not expected to know how to do everything practically, but a knowledge of the theoretical basis of techniques is usually expected. E.g. in an organic lab you should understand the principles behind chromatography, even if you've never run a TLC or done a column.
The most important thing: If you are unsure,
always ask. It is better to ask a stupid question than to cause a stupid accident, needlessly waste an experiment or damage expensive equipment through ignorance. If you don't understand why you are doing something in a protocol, stop and find out why you are doing it - this way you will understand where to apply different techniques when you begin planning your own experiments.