As the author of a work, you automatically hold copyright from the moment of creation unless you choose to transfer the copyright to someone else in a signed agreement. It is important to note that unless you retain your rights as part of the agreement you may not be able to copy & distribute to your students & peers or make it available via website, repository, etc. The process of transferring rights is not all or nothing, so it is important to know exactly what rights you are giving the publisher and what rights you are retaining.
When you are presented with a publisher's agreement, you have a number of options:
Be sure that you understand the terms before signing any agreement! You are able to make changes to the agreement to ensure you retain certain rights. The Science Commons Scholar's Copyright Addendum Engine allows authors to retain the necessary rights to reuse their research.
It is possible that the publisher will not be willing to accept the addendum to the agreement. If this is the case, you can explain why it is important to retain certain of your rights over the work. If the publisher refuses to negotiate, you have other options, including: