"I look forward to..." has to be followed by a noun (as in "I look forward to lunch"). The "-ing" form of a verb can handily act as a noun, meaning "the act of doing whatever it is", and so can fit the sentence. The same goes for any sentence where a noun is required after "to" -- such as "I can't get used to being single again", "I admit to eating all the pies", etc.
"I look forward to read your sentence" is wrong because "read" can't act as a noun (at least, not in this sentence).
On the other hand, "I want to..." has to be followed by a verb infinitive. So, "I want to go" is correct, but "I want to going" is wrong. The same goes for any sentence where a verb infinitive is required. For example: "I can't begin to understand it", "He failed to finish the race", etc.
I don't know of any way to tell which constructions are in the first class and which in the second except by learning them individually. But if you know that the sentence will work with another noun -- for example, you know that "I look forward to lunch" is correct -- then that should tell you that the "-ing" form of the verb is required (famous last words...!)