The rights for digital distribution of music are similar to the rights for distributing CDs or tapes. Basically you are making copies and selling them. The rights for this activity are called "mechanical" rights with the term dating back to when records were played mechanically, on a turntable with a needle. There are companies that are licensed to issue rights for a large number of songs, smaller publishers that hold the rights to the songs of a few artists and artists who have retained their own rights. You must determine who holds the rights for the music you want to distribute and then sign a contract for the rights.
Make a list of the music you want to distribute. List the pieces by song, by artist or by publisher. Check who holds the mechanical rights to individual songs, to the songs from an artist or to the music from a particular publisher. Start by contacting agencies, such as the Harry Fox Agency (harryfox.com), and perform a search for your songs using the Songfile feature on their website. Note down the music for which the agency can issue licenses for mechanical rights. Contact individual publishers found on the Association of Independent Music Publishers website (aimp.com) and note who has the mechanical rights for particular artists or songs. Contact individual artists through their publishers if they hold the rights themselves.
Request mechanical licensing contracts for digital music distribution from all the sources you have identified. Keep track of the responses and eliminate songs from your list if the mechanical rights for digital distribution are not available or if the rights holder does not respond. Review the contracts you obtain to make sure you can fulfill all the conditions. Get legal advice if some conditions are not clear. Negotiate terms with smaller publishers or some individual artists, but agency contracts and contracts with large publishers tend to be standard without the possibility of change.
Prepare a final list of music for which the mechanical rights for digital distribution are available, and for which you wish to sign a contract and obtain a license. Sign the contracts and get back signed copies. Put in place procedures that will enable you to fulfill the requirements of the contracts and show that all the conditions have been met. Keep track of sales and revenues, prepare regular accounting and make regular license payments for each of the contracts. Make sure you can show that all requirements have been met and that all payments have been made made.