Laptop keyboards are always getting dirty, and can be very tricky to clean, as they are made up of a number of small parts. It is advisory not to take the keys off the keyboard when cleaning, as although this may make cleaning easier, it can be difficult to get the keys back (and in the correct place!).
To clean in between the keys, use a can of compressed air. This will gently blow the dirt out of the keyboard. Try to direct the air so that it blows the dirt away from the laptop rather than just into other areas of the laptop as this can cause damage.
The laptop also has many other areas around the keyboard that need to be cleaned, such as drives, ports and touchpad. For these areas use a cloth that is 100% cotton, and does not contain stiff filaments. A cloth with stiff filaments may cause permanent damage to the touchpad, and cause it to function incorrectly. If desired the cloth may be lightly dampened.
Cleaning the laptop keyboard on a regular basis will ease the process of cleaning as the dirt is likely to become more lodged into the gaps between the keyboard the longer it is there.