Varnish is very easy to do. You might hear horror stories about the varnish rippling or dripping, or anything else you could be afraid of happening. The truth is, varnish is not paint and should not be thought of as paint.
When you apply paint to a surface, your goal is to cover the surface with a pigment. In order to accomplish this, you need to apply a sufficiently thick coat of paint, and many of them. You will hear people talk about applying thin coats of paint to avoid runs and drips. Varnish is the same in this regard; you want to apply thin coats of varnish to avoid runs and drips.
The difference between paint and varnish is the thickness of the coats and the number of coats needed. A thin coat of paint is actually a very thick coat of varnish. You usually apply 2 to 3 coats of paint for full coverage and to fully pigment the surface. With varnish, you are looking more at a dozen coats, each super thin.
The ideal thickness of varnish is so thin that it hardly covers the surface. The wood will still appear poorly coated after the first coat because the brush was rather dry and you didn't apply enough varnish. This is actually good.
This super thin coat will dry without any risk of drips, runs, or crinkles. It will dry into a smooth and hard layer that is ready for the next coat. As the coats go building up, the varnished surface will begin to shine with the beauty of the wood.
To recap, you simply want to apply a coat that is so thin that it feels like its too thin. Your brush should be as dry as if you just ran out of paint and are trying to spread what is left in your brush all over the rest of the surface! Each coat builds on the last, and it takes about 12 coats to get a finished product.
Since it is impossible to dip your brush into a can of varnish and have it come out dry, there is a trick to achieving this super thin coat. I simply dip the tip into the varnish a quarter of an inch (about 6mm), then I wipe one side of the bristles on the rim of the can as I extract it. This wipes the amount of varnish on the brush down by half. I then take this super dry brush and stroke across the grain on the wood to put a thin little puddle of varnish on the wood. As I slide across the grain, the brush will run out of varnish and become completely dry. You will see that no more varnish is present and you simply have a thin streak on the wood. I then brush over this streak with the grain to spread it out until that entire area feels dry and the brush is sliding over the area without effect. I then move to the adjacent space and repeat.
It pretty much feels like if you are "not" varnishing the wood 12 times with a dry brush. While it may seem labor intensive to coat something a dozen times, it really goes quickly since there is not much being done each time. Since the coats are so thin, they also dry quickly, allowing for faster recoats, and there is no sanding between coats because they are so thin. After around 3 or 4 coats, the wood will really start to look pretty. Around 10 coats, it will look almost perfect. Around the 12th coat, the wood will be gorgeous and protected by a waterproof finish!
While varnish may not be touted as a waterproof finish, it will become so with enough thin coats. I have finished a piece of red oak (a very thirsty wood that should never be placed near water) in my shower, where it has received a daily dousing of hot water for the past 4 years and it has never formed any stains from getting wet, even though it is right next to the shower head and gets soaked each time I shower.
This finish will go wearing down over the years, and it would behoove you to reapply new coats if it ever gets looking a bit thin.
That's all it takes to varnish a piece of wood! A dozen "bone-dry-barely-there" coats.