I've been honing tools for a little while now so I'll give this a shot. The decision to hone or not is up to you. Many experienced machinists don't bother. I do it because the tool cuts easier, more accurately, finishes finer with fewer surface defects from an unground edge and they last longer. I don't usually regrind a tool beyond the initial grind. I hone them until my rake angles are no longer effective and I throw them in a bucket; this can take 10-15 years to occur. Until then, a honed tool cuts like new.
It is important to grind a good tool. This means your tool has a geometry that you feel will work for you and that the faces of the tool are not full of facets or grind marks. If you have these defects it will take you a long time to get rid of them so grind the tool well.
It is also important to understand that you are not honing to produce an edge. You are honing the three faces of the tool so that they are dead flat, or at least the upper and lower edges are flat and co-planar to each other on a tool ground on a wheel. The edges are precise intersections between these flats and by flattening each face, the edges take care of themselves. When all three faces are flat, the edges will be very sharp and will not reflect light. If you see light reflecting off an edge then that means one of the tool faces is not flat.
You can use water or oil or diamond stones to hone. Sand paper does not live long enough to be an effective medium for initial honing, although you can use it for touch ups. I usually prefer diamond stones for most sharpening/honing but for fine finishing tools or gravers, I go from my extra-fine diamond to a fine India stone and then to a Translucent Arkansas stone. This puts a mirror finish on the tool and it cuts like a razor.
For honing lathe tools, I use a steel backed diamond stone. I prefer a 6-8" bench stone for initial honing and the credit card sized ones for honing between uses. A few seconds of attention to each flat before the tool is put away keeps my tools sharp and ready to go whenever I am. I stay away from plastic-backed diamond sharpeners for lathe tools; they flex under pressure.
I also use water with a bit of Dawn soap or a wetting agent in it to lubricate. This helps flush debris away and keeps the stone cutting well.
Again, the goal is to produce a very flat surface on each face. I usually start with the side cutting face. My personal technique is to hold the stone in my left hand (I am right handed) and the tool in my right hand. I get the face flat in both the vertical and horizontal directions, lock my wrists and apply moderate pressure on the pull stroke only. A diamond stone cuts best under light to moderate pressure; high pressure only wears the stone and doesn't cut any faster. Let the stone cut. I hone over a container with water/wetting agent or soap in it and dip the stone after a few passes. The goal, again, is to flatten the face and I check it often to make sure I am doing exactly that.
I start with a coarse diamond stone, then go to a fine stone, then an extra-fine stone. The goal is to produce a homogeneous surface across the entire face. Once you get that, move to the next grade and do it again, and again for each face.
Once I get the side flat, I move to the end and then the top. The process is the same - get the face you're honing set dead flat on the stone, make sure your wrists are locked (locked, not rigid) so your tool angles don't change and hone on the pull stroke with moderate pressure. I find that applying pressure on the push stroke works too but the tendency to roll the tool and grind down an edge happens too easily so I avoid doing that.
For me, the hardest face is the end face. The surface area is very small and it is difficult to feel when the tool is flat on the stone. It helps to color the face with a Sharpie so you know when your wrist angles are right and then try to maintain it. It takes a bit of practice to do this so stick with it.
Once I have all three faces dead flat, I create the nose radius with a extra-fine diamond stone and then take a final pass on the top face of the tool to eliminate any burrs that may have formed. Then I check each edge under light to be sure there is no reflection. Then I know the tool is sharp and ready to go to work. My freshly honed tools will cut curlicues in newsprint and they will definitely cut flesh so be careful with them.
That's basically it - hone for the flats.
Hope this helps.