When a magical portal to another world suddenly opens, an invading military force consisting of mounted cavalry, dragon-riding knights, and conscripted orcs pours through an begins a surprise attack on the unwitting citizens of a peaceful city. It sounds like the plot of the original Warcraft, except the city being attacked is Tokyo. As the slaughter begins, viewers of GATE will start to ask themselves, "why doesn't the military show up and do something about this?" It is at about this time that the Japan Ground Self-Defense Force (SDF) force actually shows up with guns, tanks, and helicopters. The invading army suddenly realizes that they have chosen the wrong world to attack.
After completely decimating the invasion force, the Japanese Government fortifies the area around the gate and sends an expeditionary force to the other side. Essentially they find that the other world is a generic fantasy realm that seems to have come right out of a JRPG. Despite knowing that their invasion force was completely lost, the emperor of the realm decides to try to repel the SDF by sending tens of thousands of men to attack them. This goes about as well as expected, and the initial assault force is immediately incinerated. Rather than deciding that it would be best to run away from an enemy that can rain destruction from the sky, the commander of the assault decides to try a sneak attack at night, proving that even in fantasy-land, learning curves are for pussies.
After basically completely obliterating what appears to be a good chunk of this world's armed forces in less than a day, the SDF decides that it is time to send a small unit in to make peace with the locals. Lead by the main character, they end up earning the trust of some peasant villagers by blowing away a giant dragon with a missile launcher and impressing them by showing off their base (which has running water and WiFi). They end up picking up a young sorceress, an elf girl, and an insane goth-loli priestess of murder along the way. Aside from the sorceress (who inexplicably learns Japanese rather quickly and begins to act as a translator) these characters seem to be there primarily for the fan-service factor. Back the the real world, there are hints of what could be a more interesting political subplot in which the United States, China, and Russia are scheming as to how they can best gain access to the magical land and exploit its resources. Focusing on this might have made for a more intelligent story, despite the fact that the entire premise of this show is somewhat silly.
Honestly, this anime is ridiculous. Pitting a society whose greatest technological achievement is the printing press against a 21st. century military is basically War on Easy Mode. Even tough the fantasy world seems to have some magic users and dragons, they are utterly powerless to do anything but gaze upon modern machines of war in awe and terror as they are mowed down by gunfire. At the same time, there is a certain amount of morbid comedy to watch an overly smug, JRPG-style empire ignorantly try to deal with an enemy that has a 1000 year technological advantage against them. They are also pretty darn lucky that their magical gate opened up in Japan. One can only imagine how screwed this empire would be if they had tried to invade Russia.
Ultimately you can't feel too much sympathy for the empire. As it turns out, the emperor is basically a jerk who seems either ignorant or uncaring of the fact that the world he tried to invade could turn his entire nation into a crater with the push of a button. Even as his advisors and senate explain to him that they are utterly screwed, he displays unwavering confidence that his empire is eternal. Either he's crazy or has some sort of ace up his sleeve, though currently I'm betting on the former.
The emperor also seems to hate his princess-knight daughter, who he sends on a suicide recon mission to scout out the enemy. Circumstances force her to accept the help of the SDF against a bandit army which is laying siege against a city. During this battle, she realizes that the SDF could end the empire after she witnesses them send in air-support to deal with the scenario. The best she can do is try to negotiate some sort of peace treaty with Japan, though it is doubtful her father will end up going along with it. This siege also contains the most entertaining part of the show, in which the bandits can't even load their giant arbalests before a chopper wtfpwns them.