In order to analyse market share, you must first understand what it is. Market share is the percentage of a market that is owned by a particular company.
This can be determined by dividing the company's total sales revenue by the total sales revenue of the entire market.  Or in SEO terms, how big a share of all searches or clicks it is capturing (ranking for).
There are a few different ways to analyse market share. The first way is to look at it historically. This can be done by looking at the company's market share over a period of time.
The second way is to look at it geographically. This can be done by looking at the company's market share in different countries or regions.
The third way is to look at it by product category. This can be done by looking at the company's market share in different product categories.