To conduct a Competitive Analysis, a good way to start gathering data is to set a framework and identify factors for the analysis.
We use a spreadsheet (with for example the following columns: value proposition, elements of main navigation, content types, main functions). Next to filling in a spreadsheet, we also save screenshots of the main userflows and key screens, and comment on them. Next to defining the assessment criteria, it is also important to collect as many competitors as possible: 2 or 3 competitors can be enough (and obviously there are cases when you have only 1 competitor or no competitor at all), but the more is the better.
This is how we search for the competitors: first, we define search keywords, try different permutations. Then we write a long list, and choose the most important 5-10 competitors. We try to have a panoramic view of your competitors: include not only the main players on the market, but the new services as well. We also zoom out: for example when we conducted a Competitive Analysis for a second hand game console marketplace, we established that not only the console and console game trade (sell/buy) services are the competitors: we included all of the online used stuff marketplaces regardless what kind of items can the users sell or buy. Even in the case that you are building a service which target audience is limited to one country, it is worth to check out the similar services offered in an other country or internationally. We know that different markets mean different user behavior, but these services can serve as a starting point, and help broaden your view.