Instead of hitting Enter at the end of a line, hit Shift+Enter to insert a
line break (<br>). The result is still a single paragraph with no spacing
between the lines. The resulting HTML looks like this:
<p>First line of text<br>
Second line of text</p>
And can be used as many times as necessary:
<p>First line of text<br>
Second line of text<br>
Third line<br>
etc.</p>
The "double spacing" is automatic and will always happen between paragraphs.
Ever since the beginning of time - well, Internet time, but that's all that
matters

- this:
<p>Some text</p>
<p>Some more text</p>
has been interpreted by the browser to mean, show the first paragraph, add
some whitespace, show the next paragraph. This is because reading tightly
condensed text on screen can be difficult. If you're putting up a long text
piece, leaving the default behavior is best.
But if you're just trying to tighten up bits of text, the Shift+Enter trick
is what you need.
Good luck!