In a tab when there's the fret number like this 7/

What does the / mean?Do I pick the note, then slide up the fret board?

it means to slide so if its like 7/10 you slide to 10 and so on.
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I mean if it just has the fret number and the /

It doesn't have another fret numer.
Listen to the song, what does it sound like they do?

Either it's a what you thought, or it's a mistake in the tab.
Usually means a quick slide if there is no number following it, but listen to the song and try to work out whether it goes higher or lower in pitch and just try to replicate it. You probably only need to slide a couple of frets up or down. The idea is to not let it sound like you're ending on something, so you have to make the note die out when you end the slide (usually by gently lifting off the neck to mute it).
Might take a while to get the hang of, but you've just got to try and copy what you hear.
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sometimes, you might just slide up the neck really fast. not to any specific fret, just all the way up. just listen to the song and try to figure it out. figuring this stuff out for your self will definitley lead to better playing however.
Is this from a certain tab or is 7/ just an example.
it means slide to nowhere

pretty much, just slide to as far as you can go then let go of the note, dont let your resting point ring out.