Layer lines are generally present on FDM prints making post processing an important step if a smooth surface is required. Depending on your print, you may end up with 3D printed model with support, hence support removal is typically the first stage of post processing for any 3D printing technologies that require support.
After supports are removed, sanding can be done to smooth the part and remove any obvious blemishes, such as blobs or support marks. The starting grit of sandpaper depends on the layer height and print quality; for layer heights of 200 microns and lower, or prints without blemishes, sanding can be started with 150 grit. If obvious blemishes are present, or the object was printed at a layer height of 300 microns or higher, start sanding with 100 grit.
Once the print is properly sanded, the print can be primed. Priming should be done in two coats, using an aerosol primer. Once priming is complete, painting can begin. Painting can be done with artist acrylic paints and brushes, but the use of an airbrush or aerosol can will provide a smoother surface finish.
The primed surface should be buffed and polished then cleaned using a tack cloth. Paint the model using very light coats; the first few layers will look translucent. Once the paint forms an opaque layer (generally after 2-4 layers), allow the model to sit for 30 minutes so the paint can set. Gently polish the paint layer with the nail sticks, and follow this process for each desired color (polishing between every layer of paint).