Analytical chemistry is a branch of chemistry. It tries to analyze chemicals in different things. A sample job would be trying to see how much zinc is in a piece of brass. There are several tools, like chromatography, that analytical chemists use. Flame tests can be used for a basic analysis.
Qualitative analysis finds what chemical species in the sample. Quantitative analysis finds out how much there is of each component in the substance. Components are often separated before this analysis.