Mine fields are a one of your most powerful defensive weapons. They will destroy every ship in the system unless neutralized by a mine sweeper. This power comes with a price though — when the mines explode they will also kill half the population of that planet. Mines therefore tend to be a weapon of last resort. Also, since mines cannot move so they must be used in the same system they were built.
One important factor about mine fields is that it only takes one mine to set off the explosion, no matter how many mine sweepers the enemy has. If the mine sweeper survives, your mine is neutralized. If it is destroyed and other ships survive, the mine will explode. Many players tend to build several mines in the same system, but this is unnecessary. Use the resources instead to build cheaper satellites or attack ships.
Laying a Mine Field
Despite its drawbacks, there are several ways to utilize mine fields. Probably the most common is using it along with a sat wall or stationary fleet of other ships. You do this in situations where you are unsure about whether your fleet is strong enough to stop the attack. If the attacker does win and your fleet manages to destroy all attacking mine sweepers, your mine will kill the rest of his ships and prevent them from nuking your planet.
A second way of using a mine field is as a deterrent. A single mine can bring an entire fleet to a halt if it doesn't contain a mine sweeper. Building the mine before the fleet enters your system can often dissuade an opponent from sending their fleet in. Building the mine on the turn their fleet is nuking will destroy the fleet. The best case here would be if the attacker doesn't know you can build mines and you set the build after he has already set his ships to move into the planet.
Just the possibility of a mine showing up in this situation makes most experienced players cautious. They often will (and almost always will if they see the mine ahead of time) send in only part of their fleet to blow up the mine, thus leaving the remainder of their fleet to walk in the next round and nuke the planet – which is most likely no longer a builder. You should therefore build several other ships to defend along with the mine. This may not stop the enemy from moving in and exploding the mine, but it will mean that he will have to send in more of his ships to guarantee that the mine is destroyed... which will mean fewer ships coming at you the next turn.
You play a type of cat and mouse game in determining how strong to build your mines. A BR-1 mine is just as effective in blowing up enemy ships as any stronger mine, so if you plan to build one in the middle of a large sat wall that is how you should go because the mine (no matter what its BR) will not detonate unless all other friendly ships in the system are destroyed. If the mine is alone or with only a few other ships, though, you have several options. If you expect the mine to go off, then a BR-1 mine is enough. But, even if the opponent doesn't have mine sweepers, the mine will not explode unless it is destroyed. Therefore, if you build a BR-3 mine and the enemy attacks with only one BR-2 ship you will destroy his ship and the mine will not explode. This then saves your population and costs him both a ship and a turn.
While I tend to build BR-1 mines in most situations, the key is to not be predicable — if your opponent realizes you only build BR-1 mines then he knows all he needs to sacrifice is one ship to explode the mine. Keep him honest, make him waste as many ships as possible on your mine.
It's a Little Known Fact...
One misunderstood aspect of mine fields is their relationship with cloakers. Cloakers may exist in the same planet as the mine and remain undamaged as long as they remain cloaked and as long as the mine is not set off by another ships. However, if another ship does cause the mine to explode, the mine will destroy ALL ships in that system, including the cloaked ship.
One little known and little used tactic is to pop trick as a mine is set off. Knowing that that population is going to be cut in half, you can set the population of the other planets for a mini-trick, which will bring the planet being attacked back up to full strength the next turn. This can be very frustrating for an attacker who sends in part of his fleet to blow the mine and expects the planet to be an easily nukable non-builder the next turn.
Note that while a mine field must be built on a planet with 50 or greater population, it techically does not need that large of a population to function. One unusual defense might be to temporarily make a small-resource planet into a builder, create the mine, and then reset the population back to the lower level. This in essence provides a line of defense for a planet that would normally have none...and might cause the enemy to waste time wondering how in the world you got the mine field there in the first place.