As a new player did you ever wonder how the opposition could muster huge fleets while you could only build a few ships at a time? Well, that's probably because you had read one of the popular strategy guides which told you to watch your maintenance ratio and never let it drop below 1.0. Well, that guide is completely wrong. The advice was based on the prevailing strategy used several years ago, not on the actual game mechanics, and to employ that strategy today is virtual suicide.
Overbuilding was once the domain of a few scarred veteran players, but today has become commonplace and probably necessary to win against experienced players. Simply put, overbuilding is where you build more ships than you can maintain at full strength, and allow them to repair over the next round or two by not building anything else. For example, assume you build 10 ships, which takes you to a maintenance level of 0.4. These ships would be vulnerable to attack the turn after they are build, but if you have sufficient econ they will be at or close to full strength the next turn.
Such overbuilds can be either offensive or defensive in nature. If you see a large fleet coming toward you then you might have no other choice than overbuilding to match their numbers. On the other hand, overbuilding is now the standard way of launching a major attack. A slow, gradual buildup of forces can be seen and countered, but the enemy might not be able to counter a sudden and significant build. This is especially the case where you have an economic advantage.
Note that this strategy is very costly on your tech development; such builds will drastically reduce or even drive tech development to the negatives for that turn. You should therefore understand how and when to overbuild — don't waste the resources of an overbuild unless you plan to use the fleet you create. If you have the time, a slow and gradual buildup is usually more efficient.
Overbuilding is very complementary to the rolling stargate attack that I often use. Note, however, that overbuilding with the added cost of maintaining a gate is very hard on your tech development. To employ these two strategies together you have to make sure to stay aggressive, and you have to keep nuking enemy planets to force him to build more ships with fewer resources. A stalemate is a losing proposition because the enemy's tech level will be increasing faster than yours and he will soon have a higher BR.
You can actually calculate an overbuild and see how many ships of what BR you can build and have them return to full strength the next turn, but I don't play SC as a math exercise. With a little experience you can usually judge fairly accurately whether your build is too much or if you can build more. A good rule of thumb is that you can build down to about maint = 0.4 for ships of BR-5 and lower. For higher BR ships I would stay in the 0.55 - 0.65 range, the exact figure increasing as BR increases. All this, of course, will also depend on your economy score — the higher your econ the more you can build.
One last word about the timing of overbuilds. From personal experience I would recommend not starting to overbuild until late in the BR-2 range. If you can start there and force your enemy's hand you will often be able to beat him to BR-3 and really get the upper hand. Note that I have seen one veteran being nuked by a fleet of overbuilt BR-1 ships, but this is extremely dangerous. If the enemy manages to get BR-2 before you nuke them then your fleet is toast. If they beat you from BR-2 to BR-3 you can usually handle it, but an early overbuild takes so many resources that recovery is unlikely.