The slide is one of the simplest guitar techniques. There are two kinds of slides: shift slides and legato slides.
The first slide pictured is a shift slide; the second is a legato slide. A few tablature writers do not distinguish between the two slides, using only shift slide notation. The abbreviation "sl." for slide may be omitted. When sliding from a higher fret to a lower fret, the slanted lines are usually changed to have a downward slope instead of an upward slope, to emphasize the sliding "down". It is possible to slide up from an open string, but this often does not sound as clean because this requires a hammer-on at the first fret (or for really fast slides, a higher fret) before sliding up. Likewise, it is possible to slide down to an open string but it requires a pull-off at the first (or some other) fret.
In Internet tablature, a slide from the third fret to the fifth might be written like any of these:
3/5 3>5 3>s>5 3s5
Internet tablature rarely distinguishes between the two kinds of slides.
Less commonly, tablature can instruct the guitarist to "slide into" or "slide out of" a note. In printed tablature, they are notated identically except, in the case of slide-into, the first note is omitted, and in the case of slide-out-of, the second note is omitted. In other words, the note slides in from nowhere, or out to nowhere. It simply tells the guitarist to quickly slide from or to an arbitrary point, usually only a few frets away.
Good sliding keeps the new note audible, while keeping the note in tune. If you don't press the string hard enough, you mute the string or buzz it on the frets. Too hard and the string bends out of tune. The latter does not happen often, but sounds awful and should be avoided.