Hi Lee
This is the way I do it - others may have different methods.
Firstly, I would apply a coat of sanding sealer, the sort that dries clear. When you apply it, it should have a milky consistency but don't worry about that - it'll dry clear. Once it's dried, give it a very light sanding because the grain will have been slightly raised and it'll feel rough. Sanding sealer is quite cheap and it helps to fill the grain so that the wood loses its absorbency. As a result, you'll use less paint and there'll be less risk of a blotchy or smeared finish.
After sanding, paint the image and let it dry. Acrylic paints are a 6ugger for running when you apply varnish over the top with a brush. If you must apply varnish with a brush, use one stroke over the paint and let it dry. Again, sand the piece very lightly and apply a second coat of varnish. Of course, you can apply the second coat as per normal and not worry so much about the paint running because the first coat will have sealed it.
I don't use brushes when applying varnish over acrylic, prefering to use a clear aerosol lacquer such as those available from Halfords and other motor car factors. Again, take care with the first coat and make sure it's applied lightly. I then leave the first coat to dry completely before applying subsequent coats directly over the top without sanding between coats. The beauty of using an aerosol is that the lacquer is applied in droplets (rather than brush strokes) so the opportunity for the acrylic paint to smear is minimised.
Other people will have different techniques, but that's worked to my satisfaction for decades.
Gill