Open access (free access without request) publications are an easy way to start practicing open science. There are two type of open access, green and gold. Both are open, and both work to give folks open access to papers.
Gold open access
Gold open access is a publication that is open access from the journal that it was published in. There are several open access only journals, and many other journals will offer open access for an additional publication fee. However, gold open access might not be the best option for folks who want to publish in a specific journal for tenure concerns, agreements with collaborators, because more folks might read the paper if it was in a specific journal, etc.
Green open access
Another option for folks who still want to make their papers open access, but are under some other constraint that prevents gold open access is green open access. Green open access is making a publication open through archiving the paper through another means, such as posting it on figshare, or having the final draft of the paper on a preprint server such as arXiv or bioRxiv. Green open access is great too.
Additional ways to practice open science are through sharing data (which can be placed under a publication embargo), preprints, and educational material.
A few resources for starting to practice open science: