If you are new to this subject, you should start out from the band theory of solids and how we apply that to semiconductors.
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html"
Then you can understand how pure semiconductors or intrinsic semiconductors conduct electricity.
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/intrin.html"
Then comes doping and the p-type and n-type semiconductors
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/dope.html"
Next is the p-n junction and what happends when the junction is forward biased and reversed bias. This is key to understanding diodes and transistors.
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/pnjun.html"
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/diod.html#c1"
This will make it easier for you to understand how some diodes (like the p-n junction diode) and transistors(like the p-n-p and n-p-n junction transistors) work.
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/trans.html#c1"
As chroot said, if you have any difficulties or questions following the material, you can ask here.
Finally, for some basic applications of transistors, you can check out how the transistor is used in an Amplifier circuit and how it is used in an Oscillator circuit.
Logic gates (like AND, OR and NOT) can be implemented using diodes and transistors. You might want to take a look at that as well.