1.
Conventional (manual) approach. Open search engine web page. Enter a query. Hit "Search". Once the search results are loaded, copy them to your list (e.g., to Word, Excel, database, etc). Press "Next" button to get the next portion of search results. Lather, rinse, and repeat. Then enter the next query. Lather, rinse, and repeat until you've gathered all the search results you need.
2.
FirstStop WebSearch approach. Choose search engines to be used. Enter all your search strings. Hit "Search". If you've requested a substantial volume of search results, have a cup of coffee or attend to other important stuff until FirstStop makes all of your search results available.