There’s really only one way by which you can improve your timing and rhythm, and that’s through hours and hours of practice. You can read books about music theory, listen to masters explain how to play a waltz or samba rhythm, but unless you put in the hours of practice, you won’t make the technical connection between what your head knows and how your fingers perform.
That’s not to say that you’re completely on your own however. One of the greatest assets a piano player can have is a metronome. This will allow you to understand how fast or slow the music you want to play is supposed to be played. Select the appropriate time as shown on the manuscript of the music you want to play and then listen. Don’t attempt to play the first time, just listen to the soft ticking of the metronome as it plays the beat that you need to recreate when you start to play.
Now you try to play it at that speed. Keep the metronome ticking out the beat and see if you can keep up. If you’re trying to play a slower piece of music you will probably have more initial success in keeping in time with the metronome than if you’re trying to play a fast flowing Mozart composition. Should your chosen piece of music be more upbeat, and you find you can’t play at the required speed, go back to the metronome and set it for a slower speed. Once you can play the music at that speed, gradually increase the metronome speed until you can confidentially play it using the correct timing.
Rhythm is something that you can improve with by listening. Learn how various music forms, such as tango and waltz are performed. Learn where the main strong beats are in each measure. Once you have some idea about how the music is supposed to sound, look at your sheet music and identify where the rhythm is showing – is it captured in the melody, or is it solely in the harmony? In a waltz for example you will usually find the left hand producing the steady, 1-2-3, 1-2-3, 1-2-3 full tone waltz rhythm while the melody keeps in time but doesn’t always conform to a 1 2 3 steady basic pattern. Generally you’ll find that the right hand is occupied with many half, quarter or even less tones but the integrity of the waltz is maintained by the left harmony. By listening to the right rhythm before starting to play you’ll be more aware of keeping to the correct timing structure to maintain the appropriate rhythm.
Commitment to practice will greatly improve your piano playing technique, but especially in respect to timing and rhythm which require you to hear the music as well as play it, practice is absolutely essential. Add the regular use of a metronome to this commitment and you’ll soon feel more confident that you are playing the music with the right speed and with the right rhythm.
Of course there are excellent courses you can take on the subject of rhythms, such as the Rhythm Piano course.