C major scale

This is the easiest scale to play on a piano keyboard, the correct fingering for both hands goes as follows:

Right Hand                   Left Hand

C - thumb                    C - pinky
D - index                    D - ring
E - middle                   E - middle
                             F - index 
F - thumb                    G - thumb 
G - index                    
A - middle                   A - middle
B - ring                     B - index
                             C - thumb
C - thumb                    
D - index                    D - ring
E - middle                   E - middle
                             F - index
F - thumb                    G - thumb
G - index                    
A - middle                   A - middle
B - ring                     B - index
C - pinky                    C - thumb

If you don't know yet, the A natural minor scale consists of the same notes as the aforementioned C major, the only difference is that the A minor starts and ends at the note of A, instead of C:

A minor scale

C major scale

Another major scale that is played in almost exact way as the C major is the G major scale:

As you can see the only one key is changed, instead of the F key, you'd now play the F sharp black key.

As with the C major scale the G major scale has its equivalent scale in minor tonality, and this is the E natural minor scale .

Being able to play just these four scales accurately will enable you to improvise on very many themes and jam tracks, as those tonalities are used quite frequently espeacially in pop and rock music.

To work on your improvisational skills you can play the scales in sequences too, in both ascending and descending motion. for example, you can play the C major scale in two note sequence:

C-B   D-C   E-D   F-E   G-F   A-G   B-A   C-B...

An example of three note sequence:

C-D-E   D-E-F   E-F-G   F-G-A   G-A-B   A-B-C...

Feel free to modify these sequences as you see fit and create your own sequences and patterns - this is all you need to know to start improvising.

Another scale that I suggest you to master sooner rather than later is the C major or A minor blues scale. Playing sequences and patters based on this scale sounds well with many different kinds of music, including flamenco and rock, not just blues.