How do I apply for a patent for an invention that is based on an already patented technology?

That is a difficult question to answer in a generic manner, as all "inventions" depend on the very specific facts of the particular development. Generally, to be patentable in the chemical arts, the progress must be novel and unobvious. Effectively, the result obtained should be new and unexpected. However, if the result was predictable but the benefit from the result greater than expected it could also qualify as unobvious. Some predictable but difficult to obtain results are also patentable. There are many other basis by which a chemical advancement may qualify for patent protection but it would be necessary to discuss specifics before an evaluation could be made.