Ernő Rubik was born in Budapest in 1944, his father (Ernő Rubik Sr) was an engineer and glider designer; his mother was a writer and artist. He pursued sculpture for a time before studying and earning a degree in architecture in 1967. Soon afterwards he became a teacher in the interior design department at the Academy of Applied Arts and Crafts in Budapest.
When he was 29 years old in early 1974, Ernő Rubik was teaching 3D design at the Academy of Applied Arts in Budapest. He was interested in shapes and liked to play with various cardboard and wooden figures. Around April 1974, he was pondering the ways in which the cube can be cut and divided, and became interested in the structural problem of whether the blocks could move independently without falling apart. He made a 2×2×2 cube which consisted of eight wooden cubes with holes drilled diagonally through them and joined together with rubber bands. Though the rubber bands soon broke, they lasted long enough to show that the cube made an interesting puzzle. Over the next six weeks he developed the wooden prototype for the 3×3×3 Cube. Upon scrambling the Cube he was afraid that it might be unsolvable except by precisely undoing all the previous moves, which would make it an impossible and uninteresting puzzle. It took him over a month of hard effort to solve the Cube. He started out by aligning the eight corner cubes correctly, and then discovered various sequences of moves for rearranging just a few cubes at a time.
Rubik applied for a Hungarian patent on his Cube in January 1975. He first approached Politechnika Ipari Szövetkezet (a Hungarian cooperative which manufactured plastic chess sets and similar games) around March 1975. He received Hungarian Patent HU00170062 for his cube in March 1977. Politechnika eventually supplied an initial order of 5000 cubes in late 1977. They were sold under the name "Bűvös Kocka" ("Magic Cube"). In February 1979 Tibor Laczi (a Hungarian businessman resident in Austria) took the Cube to Germany's Nuremberg Toy Fair, where on the final day, it was noticed by Tom Kremer the founder of the UK-based Seven Towns trading company, and Kremer arranged a worldwide deal for Rubik's Cube with Ideal Toys in September 1979.
In January 1980 Ernő Rubik travelled outside Communist eastern Europe for the first time to help Ideal promote the Cube at the international toy fairs. Ernő Rubik continued to design puzzles in the 1980s, most notably Rubik's Snake in 1981, and Rubik's Magic in 1986.
In 1982 he created the Rubik Scholarship Foundation and the Rubik Innovation Foundation to aid Hungarian designers and inventors. He founded his company, Rubik Studio Ltd., in 1983, and became its managing director. In 2017 he founded the Rubik Speedsolving Association to promote speedsolving, to support competitions, competitors and organizers as well as introducing of puzzles in education.
Ernő Rubik was the first person to solve the Rubik's cube, taking about a month to find a solution after creating his wooden prototype in 1974.
Evidence for Ernő Rubik's solving method comes from two sources. The first is David Singmaster's 1980 book Notes on Rubik's 'Magic Cube' (5th edition). On page 40 he briefly outlines "Rubik's original fast method":
D corners, U corners in place, then oriented, three D edges, three U edges, the other D and U edges, then the middle slice edges.
I had the opportunity to travel a bit with Mr. Rubik in 1999, and I asked him to solve it for me. His method was to solve the corners of the first layer, then insert three of the four edges in the first layer. Then he solved the other four corners. Then he used the "empty" edge slot in the first layer and the unsolved "middle layer" to insert 3 of the top layer edges. He inserted the last "top" layer edge piece simultaneously with the missing "first layer" edge piece. Then he swapped the "middle layer" edges into the right locations. If any of them were flipped, he would flip them, and then the cube was solved!
This solution is by far the most "intuitive" solution I know. The only part that takes any sort of algorithm is the flipping/permuting of the LL corners, and the flipping of the middle layer edges. Thus you only really need 3 algorithms. In fact, you can even get by with one or two if you get lucky with the LL corner permutation (skipped 1/6) or the middle-layer edge flippage (skipped 1/8).
It is not certain which algorithms Rubik uses to permute edges or corners. As Dan Knights indicates, movement of edge pieces can be done fairly intuitively (with F' E F E' and U2 M' U2 M type moves etc). A simple 3-cycle commutator such as Niklas can be used for the corners.
His algorithms for orienting cubies are better attested. David Singmaster in his small catalog of algorithms (page 44) attributes the following algorithm to Ernő Rubik for twisting two corners which Singmaster named Rubik's Duotwist (page 46):
Opposite corners: (B R' D2 R B' U2)2
Adjacent corners: L' (B R' D2 R B' U2)2 L
Dan Knights in his Yahoo! Group post suggests that Rubik's algorithm for flipping two edge pieces is (M' U M' U M') U2 (M U M U M) U2
I had heard a rumor that after a month he was only stuck on the last step, flipping two edges in place. Supposedly when he finally solved it, he used this move: Rx U Rx U Rx U2 Lx U Lx U Lx U2 (where Rx means turning the middle-layer slice in between the R and L faces clockwise RELATIVE to R, and Lx means Rx inverse). I had heard that this algorithm was called "Rubik's Maneuver", because it was the crux and final step of his solution.
I told him this story, and showed him the algorithm, and he said, in his heavy hungarian accent and typically stoic manner, "Yes, eed-iz pozzible zat I invented zat."
Ernő Rubik has often been asked how quickly he can solve a Rubik's cube. His standard response is that he could solve it in "about one minute".