As any 15-year-old guy can tell you, intimate knowledge of your equipment is very important to discovering how it works.
The same applies to brewing. All it takes is a little bit of prep and it makes life a whole lot easier. The whole object of brewing is to have fun and if you are stressing about not making enough beer to fill your carboy, you are not having fun.
It's all pretty basic. For instance, you should know the capacity of all of your vessels. My mash tun will hold 8 gallons, my hot liquor tank 4.5 gallons and my brew kettle will hold 9 gallons. This impacts how I do things. If I am making something which would normally call for a 5.5 gallon sparge I have to put the extra gallon into my strike water. I actually forgot to do this on my brew this last weekend and had to run another gallon through my hot liquor tank towards the end of my sparge. It didn't effect my numbers, but did make me feel like an idiot.
Know where you need to fill your brew kettle in order to get enough finished volume to fill your fermenters. Otherwise, and I have done this, you will end up with only 4.5 gallons in a 6 gallon fermenter. I have even put painters tape on my carboys to indicate the volume levels. It makes it easier for me to know exactly where the 5 gallon mark is, so I can add my yeast starter without getting the fermenter too full.
Know how much volume there is in your kettle below the spout. If there is 3/4 of a gallon below the spout and you have exactly 5 gallons in your kettle transferring to your fermenter, you are going to be short a good fill level. Here is something I just did recently, I took my brewing spoon and used permanent marker to mark what the volume of my kettle is at 1/2 gallon increments. Before doing this, I would fill a gallon jug and pour it in my pot, making just more work for myself.
I wish I would have thought of marking my spoon years ago. If I get another brew pot I will just use a different colored marker to mark the measurements on the spoon.
Do all these measurements with water, not wort. Basically, just set up your brew system and run water through it. Something else to measure is how much volume you are going to lose because of evaporation. Depending on the shape of your pot, it can range from one to two gallons, which is a huge range when we are doing 5 gallon batches.
During brew day take good notes. I try to write everything down. Stuff like the weather on brew day impacts how the beer heats, how well it boils and the time it takes to get to ferment temps. If I have some sort of problem, I jot it down. Not just so I have more info to tell you jokers, but also hopefully I won't make the same mistake again.
Part of taking notes is knowing what you are working with. I used to just brew, not bothering to take any readings, and just figured the beer would be what it was. Granted, this is a pretty low key approach and if you don't hit your numbers you don't care because you don't know. The trouble with doing this is, if you are trying to brew a 1.070 beer with 40 IBUs and you end up with a 1.050 beer, then your IBUs will be about 60. It may not turn out to be a bad beer, but it will not be the beer you intended to brew.
Homebrewers just starting out can be easily intimidated by the chemistry of brewing, the thousands of possible ingredients and the huge variety of styles. The volume of a gallon of water is a constant and by taking the simple step of finding out how to measure a gallon on your system you will save a surprising amount of headache.