There are two versions; the original costume was indestructible because it was from Krypton and everything from Krypton was indestructible. The original costume was made from his baby blankets that his mother wrapped him in for the voyage, and Ma Kent UNRAVELLED them, because they were knitted. She she was able to knit them with ordinary knitting needles.
She had to trick baby Kal-El into using his heat vision to burn through the yarn when she wanted to cut it. (Kind of the same way he later used his heat vision and a mirror to shave.)
This way, she made separate pants, shirt and cape. Please note; Superman doesn't wear his underwear over his pants. That is just a decorative design, and so he can have pockets. (Otherwise he would have to wear a utility belt to carry cash to pay for the windows his sonic boom breaks when he flies at super speed, etc.)
In the John Byrne revamp since Crisis on Infinite Earths, the origin of the suit was changed. Things from Krypton are not automatically indestuctible any more. Kal El has super powers on Earth due to genetically implanted changes made by his father Jor El. (These relate to the Kryptonian 'warsuit' which he has in his Fortress; it is the ultimate development of weapons technology.)
Martha Kent made the costume, but it was made of ordinary Earth cloth. They changed the invulnerability to a force field of sorts (without making a big issue out of it.) Martha said she noticed when he was just a boy that clothes next to his skin never seemed to get dirty or torn.
So the costume is not ordinary cloth and his invisible force field protects it. But his cape sometimes gets torn in combat and it looks really cool shredded up, so he has to have a closet full of spare capes at home. This is easy enough, since Superman is one of the most popular costumes and he can just order them from a supplier and say they're for a costume party.
Back in the 60's, Superman temporarily wore a different costume when Luthor tricked him into thinking his original costume was no longer indestructible. I recently wrote and answer about that and you can find it, or you can learn more by going to Supermanica, the on line Superman encyclopedia.
28 MAY 08, 1613 hrs, GMT.