Will you please tell me what is the best method of playing rubato?

The artistic principles ruling rubato playing are good taste and keeping within artistic bounds. The physical principle is balance. What you shorten of the time in one phrase or part of a phrase you must add at the first opportunity to another in order that the time "stolen" (rubato) in one place may be restituted in another. The æsthetic law demands that the total time-value of a music piece shall not be affected by any rubato, hence, the rubato can only have sway within the limits of such time as would be consumed if the piece were played in the strictest time.

How to Play Passages Marked "Rubato"

I find an explanation of tempo rubato which says that the hand which plays the melody may move with all possible freedom, while the accompanying hand must keep strict time. How can this be done?

The explanation you found, while not absolutely wrong, is very misleading, for it can find application only in a very few isolated cases; only inside of one short phrase and then hardly satisfactorily. Besides, the words you quote are not an explanation, but a mere assertion or, rather, allegation. Tempo rubato means a wavering, a vacillating of time values, and the question whether this is to extend over both hands or over only one must be decided by the player's good taste; it also depends upon whether the occupation of the two hands can be thought of as separate and musically independent. I assume that you are able to play each hand alone with perfect freedom, and I doubt not that you can, with some practice, retain this freedom of each hand when you unite them, but I can see only very few cases to which you could apply such skill, and still less do I see the advantage thereof.

Perfect Rubato the Result of Momentary Impulse

In playing rubato do you follow a preconceived notion or the impulse of the moment?

Perfect expression is possible only under perfect freedom. Hence, the perfect rubato must be the result of momentary impulse. It is, however, only a few very eminent players that have such command over this means of expression as to feel safe in trusting their momentary impulses altogether. The average player will do well carefully to consider the shifting of time values and to prepare their execution to a certain degree. This should not, however, be carried too far, as it would impair the naturalness of expression and lead to a stereotyped mannerism.

The Difference Between Conception and Rubato

Is there any difference between conception and rubato?