What chord is this?

[ren]

Sorry if I sound dumb on this one, but how do you make a chord out of B, F and G?

Feel free to write down the procedure on how this is found out.

Thanks for your help!

And sorry for that obscured bit at the top left, the key sig is a B flat.

[JumpingJack]

The D comes later in the bar/measure (the C and As are passing notes).
So yeah, Gm7.

Notice the seventh eventually falls in the next bar as you would expect with good part-writing.

[ren]

Grade 8 in the ABRSM (the British musical examining board, 8 is their final grade) not academical sense

And I'm 16, started music at 6

[Dave Draper]

Hi Ren,
The song is in the F key, so I transposed it to the key of C, just for kicks. Where C ( or F in your case) is (roman numeral) I, the chord you are asking about is (roman numeral) II with a 7th.
So when I play it in the Key of C, I'm playing a D7th to get the same sound