Accessing a search engine by going to a web page (e.g. here:
https://www.bing.com/ ) is no different to visiting The Answerbank. i.e. you come to the page, enter your information, click 'Search' or 'Submit' and wait for the server to respond.
Installing a tool bar (which is what I assume you were referring to when you wrote 'downloading a search engine') makes
a modification to your browser (such as Internet Explorer, Firefox or Chrome) that theoretically makes access to the search engine quicker (and frequently offers lots of 'little extras' that you don't need anyway) but, because it's mucking about with someone else's software, has a nasty habit of causing problems.
I've never come across any third party tool bar that really adds anything wonderful to a web browser. They're just a waste of time in my opinion.
Further, a decent browser such as Firefox already has a search function built into it anyway. In Firefox you simply enter your search terms into the box at the top right of the screen. By default it uses Google as its search engine but simply clicking on the arrowhead at the left of the box allows you change it to, say, Bing.