Saito went to Halkeginia from a portal that appeared in front of him in normal world:
At the time of the summoning, he had just picked up his laptop after attempting to get it repaired in Akihabara. Walking home a portal of some kind opened in front of him; and Saito's curiosity getting the better of him, he touched it and was sucked through.
After this, he traveled to Halkeginia and become Louise's familiar.
But this portal only appeared at Saito's world because Louise used The Summoning spell, to summon a familiar (destiny?). At that time, nobody knew that Saito's world even existed.
So, how can be explained all other stuffs from his world that appeared in Halkeginia? Like all those weapons and airplanes used by him:
SIG Sauer P226
A6M Zero fighter
Flak 88 anti-aircraft/anti-tank gun
I didn't read their manga/novels, is it better explained there?
(Weapon names and images taken from this Wiki).