The Copyright Clearance Center (CCC) is a licensing clearinghouse representing thousands of publishers. The CCC can streamline the process of obtaining rights for the use of copyrighted materials when rights are required.
Anyone can enter the CCC and check the cost of royalties based on a specific use.
To request re-use of a journal article or material (such as figures or images) in a journal article, you most often need to request permission from the publisher. Most journal articles have a link on the abstract page that says "Rights and Permission" "Get rights and content" (or similar). You may have to look for a submenu under tools etc.
Clicking this link will take you to a Copyright Clearance Center page where you can input some basic information. This form will generate a price for your re-use and a license statement that you can print out or save for your records.