Picasso is without question one of the most influential painters of the 21st century. But it took even this genius about 60 years until the so-called Picasso style evolved. He had to experience and interpret knowledge from many other fields of arts and life until he developed his own style of painting.
In his early years, like nearly every artist, he was under the strong influence of his masters; this meant mostly Munch and Toulouse-Lautrec along with the great masters of the renaissance and baroque. Then came his blue and pink periods, which showed signs of his genius, although a few years still had to pass until he "matured" as a painter.
The first and most important step in the Picasso style evolvement was when he and Braque discovered cubism in 1907. During this period, which lasted for about 20-25 years, he considered it his biggest task to prove that, although perspective works very well in portraying objects from one point of view, it is also false in a manner, since we consistently move, and observe these objects from multiple angles. Cubism's biggest achievement was that these pictures showed objects not just from one point of view, but from many. These separate angles were adjusted together and composed into one picture. This made them seem like abstract paintings, when Picasso was asked about this, he said: "cubism has absolutely nothing to do with abstraction".
After the exhaustion of cubism, the Spaniard painter turned to classicism, symbolism and surrealism, which would also help the Picasso style evolve. We can't directly associate him with either of those acts, but he did let all of them influence him. He learned to use his subconscious and he studied children's drawings, which he then used in his own works, these where methods discovered by the surrealists. He made many paraphrases of the great masters' work, for example of Goya's and Velazquez's paintings. He added symbols into most of his work, these are what make them so complex and suggestive.
He experimented with sculpting - making not only "classical" statues from wood or clay, but many ready-mades. Besides this he became familiar with ceramics while staying on the french riviera, he designed and painted thousands of plates and vases. All this was interpreted into the artist's visual language: the quickness needed to create a ceramic plate or the inspiration used to complete a ready-made sculpture.
These where the main points of inspiration Picasso used in developing his very own and very unique style. The fact that he experimented in these different fields helped the Picasso style evolve into something with such character that it has continued to influence artists and movements to this day. Although an important fact has to mentioned: in the 1950s and 60s the spaniard received a lot of negative feedback, because his paintings, were sloppy and didn't seem to be finished, only later did they admit that this was all intentional by the artist, and again well ahead of his time, he introduced neo-expressionism. His late pictures also helped inspire many abstract expressionist painters such as Jackson Pollock or Mark Rothko and keep inspiring many painters to this day.