Analytical chemistry is a branch of chemistry. It tries to analyze chemicals in things. A simple job would be to see how much zinc is in a piece of brass. There are several methods, like chromatography and mass spectrometry to do this. Flame tests can be used for a basic analysis.
Qualitative analysis finds what chemical species are in the sample. Quantitative analysis finds out how much of a substance there are in a sample. Substances in a sample are often separated from each other using chromatography before the analysis. This is because a sample can contain many different substances.