Gerek and lazım are frequently used words in Turkish, but they are difficult to translate into English. The most common translations are 'to be necessary', 'to be needed', 'to require'. Gerek is both a noun and a verb (gerekmek). It's adjectival form is used frequently too: gerekli. Let's see some examples.

gerek	Turkish	English
As a verb	Gitmem gerekiyor.	I need to go. [Lit.] My going is needed.*
As a noun	Söylemenize gerek yok.	There is no need for you to say.
As an adjective	Bütün bu eşyalar gerekli mi?	Is all this stuff necessary?

*Notice how the translation when used as a verb is very different. From now on, we will be using the literal translation to make things easier.

Lazım on the other hand is mostly used as a predicate noun. If you want to use it as a verb, it gets the auxiliary 'olmak'. Let's see:

lazım	Turkish	English
As a verb	Araban bize lazım oldu.	We needed your car. [Lit.] Your car became necessary to us.
As a noun	Kalemi bana lazım.	I need his pen. [Lit.] His pen is necessary for me.
As an adjective	Lazım materyalleri getirdik mi?	Did we bring the necessary materials?

The subject of these sentences is the thing that is needed, not the person who needs them. For example in "Araban bize gerekti." (Your car was needed to us.) the car is the subject while in reality it is us who experienced a need, not the car. Because of this aspect, these words are used to depersonalize some parts of speech, or make speech impersonal in general.

Breakdown of Gitmem lazım.