Hi, cleaning your airbrush is very very important and very hard for people to get right (strangely enough?). Anyway I dont use the cleaner that they provide (alcohol) as it thickens the paint and then theres no way you can get it out! Very annoying. I fill up a bottle with a little bit of window cleaner, or washing up liquid (just a little)and then fill it with water. Water is the best cleaner for cleaning in between colours or when you are cleaning it after using colour. You can only use the alcohol cleaner AFTER you have cleaned out all the paint. You can soak the parts in it overnight for a proper clean. But I dont do this (a-I'm lazy and b- I dont need to as I clean the airbrush properly anyway). I Always leave the little paint feeder/cup on the airbrush filled with water. Any paint left that gets dry will eventually cause a blockage.
Techniques on cleaning
1 - spray out any colour left after airbrushing before putting water in it. Shaking it/flicking it is a good way to make all the paint in the barrel come to the nozzle and therefore more paint will come out
2 - Put water in and spray out
3 - Put more water in and cover the end with your finger or cotton pad and do a 'spray back'. Basically you are rinsing the inside of the barrel. The cup will bubble from the water being sprayed back.
4 - empty water and fill again and spray out until water is clean or near enough
5 - shaking/flicking the airbrush is a good technique to use when you are changing colour as it gets more of the previous colour out. A good tip when airbrushing is to start with the lighter colours and go darker as then you dont have to clean the colour out completely in between colours. You can even just spray out the rest of the colour and then put your darker colour in, you wont see the previous colour as its lighter.
6 - leave the airbrush with water in it.
7 - regularly take off the nozzle cap and clean it and the hole that the needle comes out through. Sometimes a tiny bit of dried paint will be in that hole (miniscule...only fleas can see it) but it will stop the paint coming out properly. I remove it with the tip of the needle.
8 - Regularly clean the needle
If you ever try to clear the tiny nozzle itself (with the tip of the needle) be very careful as if it gets cracked/split you will have to buy a new one. Its good to keep a couple of spares around. Im not sure what your airbrush looks like but I think most of this will be relevant.