Contact the publisher of the work you wish to lease by researching it on a retail website, like Amazon.com. Request a mechanical license agreement from the publisher to use the published work. Note that publishers can range from large, multi-national corporations to self-published individuals.
Obtain the mechanical lease agreement from the publisher in writing, including duration of the lease, terms of the lease, i.e, what you can do and for how long, and the amount that it will cost you.
Make sure you understand the exact terms of the lease before you sign it, i.e., a mechanical license or lease agreement to use a song which states that you are allowed to make only one master copy of your own for profit and is limited to duplicating it up to 1,000 times via download, CD, or DVD.
If the exclusive rights to the work that you have previously purchased a lease to publish are sold, you will be able to fulfill the specifications of the original lease but will not be able to buy any further rights to use the work.