SLIDE UP: Play the first note then slide the same note (fretting hand) up to the next note. Don't play the second note, the sound is continued from the slide. Remember to keep enough pressure on the string so the note continues sounding when sliding, but not too much so that the slide is not smooth.
The above video shows all different types of slides, up & down, one, two & three note sliding. If your strings are a little rusty then sliding becomes a little more painful and less fluent. I sometimes prefer to use some products like "Finger Ease" or special oil rag wipes you can buy that you rub on the string to make them last longer and stops them from rusting.
It is naturally more difficult to slide with 2 of more strings, some songs even require you to slide the whole bar chord. To do this you have to be an accomplished bar chord player and be able to slide smoothly already.
SLIDE DOWN: Do the same as above but slide down instead of up