How did the styles and techniques change change during the Renaissance? What methods of artwork were created purely in the Renaissance?
When it comes to the Renaissance, it is a pretty lengthy time of period that spread across different countries. I am going to go ahead and assume that you are referring to the Italian Renaissance.
From the start, the one thing that is immediately apparent about Renaissance art compared to pre-Renaissance art is the use of the 3D perspective. Take these examples by Giotto and Masaccio, two of the first Italian Renaissance artists:
http://upload.wikimedia.org/wikipedia/commons/c/c4/Giotto,_Lower_Church_Assisi,_Nativity_01.jpg
http://upload.wikimedia.org/wikipedia/commons/b/b0/Masaccio7.jpg
You can see that both artists were attempting to capture a picture in which the background plays a integral role to the piece. Both started to pay attention to height and depth. They create a sensation of you looking out the window into another world as opposed to looking into a flat piece of paper like with a 2D painting:
Pay attention to the background. It looks almost as if the figures are attached to it. There is no dimension to them.
When it comes to what methods of artwork came out of the Renaissance, there is quite a list. A lot of the Italian Renaissance artists were greatly interested in following the lessons of the old masters from the classical world. Painting was extremely popular but so was architecture. Art became a strong industry because it promoted art patrons, which in returned gained popular support in the political arena. Patrons would often compete for artists in order for their patronage to provide the best pieces of art.
One of the styles of painting that developed out of the Renaissance was Chiaroscuro (clear-dark in Italian.) A strong contrast between light and dark was used in such paintings. Take for instance the following example by Giovanni Baglione:
Pay attention to the darkness and the way it compliments the clarity of the figures. Notice also at the bottom the way the darkness affects the contrast of the demonic figure sitting down. It creates realism and amplifies the depth of the image. We are looking at an image stepping out of the darkness almost.
While not exclusively a Renaissance discovery, many artists also became obsessed with linear perspective. As I mentioned previously, architecture became a big art industry in some cities. Architects such as Alberti invested a lot of time towards mastering it just to help them achieve a desired look with their buildings.
Furthermore, a lot of research went into mastering color in the Renaissance. The Venetian Giovanni Bellini developed a lot of techniques in order to capture certain colors in his paintings. Bellini would often use unorthodox methods to achieve his results. Ex. he would mix glassy materials along with paint in order to capture certain hues.
As you can see, there is a significant amount of art developments that came from the Italian Renaissance alone. I avoided touching artists such as Leonardo da Vinci and Michelangelo due to the abundant amount of resources on both of those artists. If you are looking for a most specific response regarding a specific artistic discipline (ex. sculpture) let me know and I will expand further.
I recommend the following books:
Painting and Experience in Fifteenth-Century Italy: A Primer in the Social History of Pictorial Style by Michael Baxandall
Renaissance Florence by Gene Brucker. Excellent read for a quick crash course on how Renaissance politics (specifically in Florence) fueled the art industry.
The Patron's Payoff: Conspicuous Commissions in Italian Renaissance Art by Jonathan K. Nelson, Richard J. Zeckhauser and Michael Spence. A more recent and up to date study in the relationship between patron and artist during the Renaissance.
