You'll start with molding with nail holes and some gaps in the corners (sorry I don't have a picture of this stage).
First you'll want to sink the nails. This sets them below the surface of the wood so that you can fill the hole left behind and make it look seamless.
Use a hammer
If you use a nail gun to install the molding you can set the "depth" of the nails to be "sunk" already and you can skip this step.
Once the nails are sunk you need to fill the holes and you might as well do the corners while you have the spackle out. In my experience filling the corners is the most important step to a seamless result, plus it hides any "Oopsies" and gaps.
I use just regular spackle like this
and my finger to apply (wash hands immediately after application). You can wear gloves if you don't like to get dirty, but a finger works much better then a putty knife for this.
After filling the holes you will have something that looks kind of like this
A bit bumpy and rough. To smooth this out you just have to sand it down. I use a fine 220 grit sandpaper, which comes in big sheets like this
I cut the sheets into a small squares to make it easy to use. You'll probably need a bunch of squares, just switch to a new piece when the one you're using gets "clogged" with paint/wood. You'll know what I mean when you're doing it.
When you're done you should have something pretty like this. Nice and smooth.
Now you're ready for a final coat of paint and you're done. Since my wall and molding will be the same colour I didn't tape anything and just painted it free hand. Also, I used a satin finish paint for the molding/wall because I don't like my trim too shiny, but I still wanted it to be easily wipeable.
I also got hubby to caulk around the outside and inside of the boxes to fill the gaps for an even more professional look, but I will plan to do this myself next time (there will be more molding!) and include a how-to for you. I'm a bit intimidated by the caulk gun since it looks like a weapon or gynecological torture tool.
But I stand by my "all women can use power tools (or non-powered tools) even the clumsy ones like me" statement. I will master it and show you how you can master it too.