It is best to clean the instrument with dry cloth after playing. The most important part of the instrument to be cleaned is the area below the strings as this is where rosin dust from the bow falls. This type of cleaning is possible only when the instrument had not collected dust mixed with sticky dirt under the strings.
If the dirt can not be removed from the varnish by a dry cloth, this should not be attempted with any cleaning liquid, solvent, or any abrasive means as your instrument's varnish can be damaged beyond full repair. Even experienced violin makers find separating sticky dirt from varnish as painstakingly difficult and tyring job, especially when one tries to avoid damaging the original varnish below. This is exactly the reason why such work, if really done expertly, may become expensive in its own right. It is therefore very important to clean the instrument regularly.
In most cases the main culprit is a low-quality rosin and its dust that falls from the bow during playing. The quality of the rosin can easily be ascertained: if we find it difficult after playing to clean away the dust with the help of a dry cloth, we can be sure that the rosin is of bad quality and should not be used. Low quality and therefore sticky rosin that usually produces a lot of dust also generates noise while playing.
High price does not necessarily guarantee the best rosin.