You can double the speed of your metronome but play at the same tempo as before. That is a simple way to have the metronome line up. In reality, music is not ridged like a metronome. A metronome can't "swing" but lots of music does. Technically "swing" gives the first half beat a little more time than the second half beat. Composers don't write all the weird timing in the notation, but will have a note at the top of the music that says Swing.
The correct answer for you question is in the time signature and bars of the music. Each bar has the number of beats specified by the time signature. The beats could be notes or rests, but a bar will always have specified the number of beats.
Time signatures can change during a song. For a friend I was working out a pop tune he wanted to play. As I started to work with it I found 7 beat bars probably noted as 7/8. I then saw a transcription and the song, as written, was a bar of 4/4 then a bar 3/4, rinse and repeat. Well, just repeat.
Then it can become really weird playing rubato (without strict adherence to tempo).
I was never trained in music theory and I can't always explain what I'm playing in music theory terms, so I hope this makes sense. Like Carol mentioned, the "feel" of the music is hard to explain or notate, but is probably the most important element in making music on any instrument. It will develop over time. I was playing swing long before I knew that's what I was doing, so for me, feel works better than music notation.