Nielsen Norman has some research on Search, and go into some detail regarding using a magnifying glass or similar icon vs. a label
The Magnifying Glass icon in search design
Summary: People usually recognize that a magnifying-glass icon indicates a search tool, even when it has no label. Unfortunately, showing only the icon makes search more difficult to find.
They mention that one disadvantage of using the icon only:
The magnifying glass alone makes it much harder to locate the search.
When used without an open-entry text field, the icon takes up less space. Visually, it’s less prominent and, therefore, less noticeable. We don’t recommend the icon-only pattern for desktop websites. Icon-only search makes sense on mobile devices, because there’s less screen space and fewer icons and labels in general. But on desktop, there’s more to look at, and thus, it’s easier for the stand-alone search icon to get lost in the crowd.
If the icon is visually prominent enough, most users did recognize the magnifying glass.
As for using a button or icon to click on:
Because many users still have the habit of clicking a Search button to submit the query, it’s essential that clicking the magnifying glass submit the query.
Their own site uses a clear label for search, and they are intentional about keeping the text label 'Search' and hitting
Enter will trigger the query as well as using the button.
as for using
Enter to start the query, you can use both the keystroke or the button as @Shreyas Tripathy has pointed out.