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 "Get rights and content" (or similar). This link is typically located under the title on the right-hand side.
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. These licenses are directed at graduate students working on their ETDs.
Look for a "Get Rights and Permissions" link on the book's webpage, often hosted by the publisher. If you do not see a link to "Get Rights and Permissions" on a book's website, then look on the publisher's website for information about "Rights and Permissions." This may be filed under headings like "Customer Service" or even "Terms of Use." Usually there will be a form to fill out and e-mail; occasionally there will be only a phone number or an individual's name to contact, for example: the Rights and Permissions page from the publisher John Benjamins.
It is a common practice to re-use images found online in journal articles, papers, presentations, and theses. While many images may qualify as fair use under the transformative use test, the best practice is to assume, always, that images are subject to copyright and that permission should be gained before using them. Alternatively, many images are licensed under a Creative Commons license that allows you to re-use them with attribution but without asking permission.