You're going to have to fill the grain.
At this point, you'll need to select a filler with either "truly clear" or contrasting color. Fill the grain, sand back, fill, sand back, fill, sand, etc... until there is no more grain to fill. One way to figure this out, is to sand smooth with 400 grit paper. The wood with its grain filled will be totally smooth and slightly glossy. You'll need to use a strong back, or side, light, in order to make sure all the grain is filled. This is the most important thing to do.
By now, you've probably sanded off a little bit of the dye you already used. Touch up your work.
Now you can apply lacquer, from spray gun or rattle-can. You may want to shoot one coat of sanding sealer, over the grain filled wood, or use one coat of shellac over the grain filled wood, to prevent the lacquer from shrinking in, but with alder, it will be minimal.
Shoot several light coats, then a medium wet coat. Let it dry two days. Another medium wet coat. Let dry two days. Keep that up for six coats. Now you need to let it dry for a week or so. After that, you can "level" the finish with 600 paper - wet. ALWAYS use a sanding block for all of your sanding - NEVER use your fingers or you'll get ripples.
After level sanding, give it two more medium wet coats. Re- level after another week of drying. Now you can polish it out. The 600 grit will polish out with compound, no need to go to 800, 1000, 1500, etc. Its just not needed. When you polish it out, you'll probably notice small places where a scratch remains from leveling. Carefully sand those smooth and polish again.
Once you have it polished, you can buff it, even by hand, with very fine compound, followed by plain ol' auto wax.
At that point, you should have a pretty nice looking finish.
