On trumpet, the way a 'half valve' is done varies widely between players and can also depend upon if the note is held in place, or moves up/down to another note. The genre of music also is a variable. It's often used in various forms of jazz playing, almost never in classical or 'concert band' repertoire.
The term 'glissando' is what happens when you slide between two notes, but you want the transition to happen slowly, instead of instantly like in a normal 'slur' where it happens quickly, without using the tongue to articulate the note sharply. Sometimes that is done with a half-valve approach as well, occasionally players will finger rapidly through the intervening notes on the way, like a fast chromatic scale. The closest thing on a string instrument like the guitar is probably sliding the hand noticeably up/down the neck between notes to draw out the transitions. Stevie Ray Vaughan (and many other blues guitarists) use(d) that technique quite often.
Some trumpet players use just one valve slightly depressed (usually the third) and not even quite half way for a simple effect on a note. Perhaps one of the most famous uses of the technique is for the 'horse whinny' at the end of the Christmas song "Sleigh Ride" by Leroy Anderson. It's an extended version of it, where the trumpet player tries to sound like an actual horse. There are also percussion instruments used to sound likes whips cracking, hooves clacking on the ground, etc.
In jazz music it's done in a lot of different situations, which may alter the pitch, or may only be used to make the note much less loud relative to those around it. Some players even use it while 'ghosting' notes so the note is there, but almost inaudible.
When you're transcribing to a new instrument, you do not have to keep every articulation mark if it doesn't make sense for the new one. Listen to a recording of the original, if possible, and come up with something on the guitar that would give a similarly interesting effect, and use that instead if necessary.
