Practice fretting the strings. The frets are the metal strips that run perpendicular to the strings that mark each note. To play a note, press your finger down between the metal strips, not on them. To say that you're playing the third fret means that you place your finger on the string in the gap between the second and third fret. If you hear buzzing, move your finger away from the lowest fret and closer to the higher fret. Hold the string down firmly so that it only vibrates between your finger and your strumming hand, with the tip of your finger doing the pressing.
You do not need long fingernails to play guitar. In fact, it's best to keep your fingernails short! As for the callouses, these may be unavoidable. If you would like to avoid them as much as possible, ask your guitar instructor about lowering the action of your guitar (the action is the distance between your strings and your frets) so that the frets are easier to press down on.
These lead guitar lessons cover everything you need to know in order to get started with playing lead guitar. You'll learn things like: proper hand technique, the Major Scale, the Major Pentatonic Scale, the Minor Pentatonic Scale, bending technique, vibrato technique, legato technique (hammer-ons and pull-offs), and even how to play your first guitar solo! So, whether you are brand new to playing lead guitar or just want to sharpen your skills - these lead guitar lessons will help.