For this purpose there are 'simple' interface boards like the HX711 (google on HX711). A guy named Bogde has written an Arduino library to manage this board which you can find on GitHub (https://github.com/bogde/HX711). There you can also subscribe to the corresponding email group, which is rather lively and also handles similar questions as yours.
Also Sparkfun sells these sort of interface boards and has very good and extensive documentation and tutorials on the site (see comment from VE7JRO below your question).
You can manage 4 load cells with one Arduino depending on the frequency with which you want to read them. If all 4 load cells are used to weigh one platform then Sparkfun sells an interface board to combine them in one "weight sensor" making it even more simple to interface with the Arduino.