After I enter a new search engine and its URL, how can I actually add it? There is no button to push, actually there are no control elements whatsoever. I will appreciate your help in this matter.
How to add a search engine:
How to use a search engine:
The other answer is out-of-date. In current Chrome, right-click the address bar, select "Edit search engines..." and scroll to the bottom of the lower list of search engines. You need to fill in the three boxes for name, keyword and URL. If any of these do not have valid text entered, they will be filled in with a grey background and there is no way to add the search engine. Once they are all white, you can press enter to add the new search engine.
There doesn't seem to be a way to add using the mouse, and the new search engine will just disappear into the big long list of search engines once added, so you need to go and find it to check it worked. You can then hover it and click the "Make default" button that appears to use it as a default search engine.
Try "Example", "example.com", "example.com/%s" to test this if you're not sure what kind of values to fill in.