Step 1: Find a reference/inspiration map showing the style you like.
Neither reference nor inspiration is really the right word for this; it's somewhere in between. I usually use the word inspiration when I post, as reference implies copying. Using this method, you're never going to get an exact copy, so there is no need to be afraid of plagiarism. Got your inspiration map? Ok. As we go, I'll explain what to do with it.
Step 2. Make your coastline.
You can skip this step if you're making an inland regional map; I find that I have a really hard time with those unless I do a continent-level first, as all of the rules I follow go out the window if you can't see the shape of your landform.
So, take a long hard look at your inspiration map. How did they do the coastline? Is it a penstroke? How thick? Is it just a border between a dark sea and a light land that isn't actually stroked at all? Is that a woodcut, or just hatching? It takes a while and some practice to figure these out from looking at a piece, just take your best guess. As you look, you're forming instructions for what to do with your own coastline. Memorize these instructions as well as you can (do not write them down), then put away the reference map.
Now draw your coastline (if you want, you can do this in pencil and style it according to your instructions later). Remember the following: Coastlines have really jaggy spots and spots that are more smooth. Coastlines have lots of protrusions and inlets, and sometimes the protrusions shelter the inlets to make lagoons. The wikipedia articles under the category "coastal landforms" are priceless for getting an idea of the kinds of shapes that coastlines can make.
The coastline, as with most of what we're doing, is trial and error. Most times I'll start with a smooth shape, and then add in detail, erasing the smoothness as I go. Sometimes that takes two iterations before I'm happy with it.
Once you have the shape of your coastline set, style it with the instructions you memorized while looking at your inspiration map. Take your ink (it'll be ok, imperfection makes a map look good, not horrible) and take your best shot following your internal instructions. After you're done, open up (or take out of the drawer) your inspiration map and compare your map to it. Did you come close? If you're so far off that you hate what you made, start over --- but I find that usually I've come up with something my own that doesn't really look like the inspiration but I like it anyway. I think I subconsciously tweak those instructions to pick out what I like about the reference and discard what I don't like. That's why I never write them down.
Once you're happy with your coast, it's time to move on to mountains.