The description I'm most familiar with, at least as far as completeness of a description, is from the DGP (semi was once canon) MT "Starship Operators Manual Vol. 1"* Paraphrased and summarized:
Going into jump the grid slowly comes to life glowing as the pattern is built. As the energy builds the area around the ship starts glowing then becoming suddenly so bright that it is painful to look at with the naked eye. Then "blink" and the ship is gone and the glow rapidly fades to a point and disappears.
Coming out of jump is the reverse. First there's a glowly haze then a point source that rapidly expands to a blindingly bright area glow and that fades revealing the ship with the grid glowing that slowly fades as lines dim in order.
Personally I dislike that description for a lot of reasons.
In MTU going into jump is a big display of raw energy as the jump drive tears a hole into jump space. The ship tumbles in as the jump drive pours energy in to hold the hole open. Then it's all black again. No warm up grid glowy effect or other stuff. Just a short lived mini-sun effect "ahead" of the ship. What you can tell from this, from quite a ways off, is how much fuel is used. So if you know the size of the ship you can guess how long a jump was attempted. But knowing where it is going is another matter.
Coming out of jump is dictated in part because of how I see it working and part because I want, nay, DEMAND, stealth by any handwave required
So in MTU coming out of jump is a very "quiet" affair. Jumpspace is a very cold place and it takes a lot of energy during the trip just to keep the ship from freezing solid at absolute zero. When the ship drops out of jump there is no flash and it carries a residual cloud of that cold jumpspace so for a brief time the ship is all but invisible to all sensors and can run dark for a time if the desire is to remain unspotted for as long as possible.
* I still curse the fates for taunting me with that implied promise of more