Instagram is arguably the biggest modern platform for tattoo artists to promote their work and gain client and sponsored exposure. However beneficial it may be when artists post their original work, it is also subject to being taken to other artists to have copied upon request of the client. This can be prevented through watermarking, distorted photo editing, and educating both artists and customers on the matter.
Pinterest is every artists nightmare, given that most links that images are saved with are reposts, broken, or not relevant to giving credit to the actual image. Pinterest items may be reposted or grouped haphazardly into folders/groups over and over, misconstruing and tainting any original credit or "link-path" to the original picture or artist. While Instagram images are linked to an original poster or user, Pinterest images are even more difficult to link to any source. Instagram is the most image-rich platform in which tattoo artists share their work on and has been used as an invaluable business platform related tool -- Pinterest isn't relatively purposed in that way.
Good Ol' Google
Upon googling "owl tattoo", 75.3 million results come up, most of which are images and "inspiration" pages where individuals can get ideas for a prospective tattoo. Google is full of reposted images, with no original source linking the work to the original artist or media. In essence, you are setting yourself up for accidentally copying an entire original work, which may or may not be subject to copyright. Tattoos do not fall under Fair Use in most of these cases. If the images are not explicitly from Public Domain, if you have not contacted the original artist for permission, and if they are not in compliance with respective Creative Commons licensing, then you are essentially falling into copyright infringement. This is, of course, if you do not change the design in such a significant way that it is discernable and unique from the "inspired" original design. The line between inspired and stolen is thin. One could argue either way.
As An Artist
As a Patron
For most religious works, it is unclear who the author or creator is, due to the fact that most religions bear the idea that their God or Gods have manifested that image. In the case of iconography, particularly in the Eastern Orthodox religions, these are merely human-made images made to represent an entity, and are not subject to copyright given that they are usually replicated. There are some special editions of religious text, such as the King James Version of the Bible, that are copyrighted entirely. In the case that you get copyrighted text tattooed on you, it may be argued that this violates copyright.
As the same goes for replica-makers, most famous artwork such as Van Gogh's Starry Night and da Vinci's Mona Lisa are public domain and can be tattooed or replicated freely. This is due to the fact that the copyright expires 70 years after the passing of the artist. After this, the artwork is Public Domain. However, for works that have not fulfilled their copyright life, many museums and trusts such as the National Gallery of Art, the Metropolitan Museum of Art, and the J. Paul Getty Trust have created high-quality digitized images of works (sculptures, photographs, paintings, etc.) that are automatically placed in Public Domain for commercial and non-commercial use. This "open-access" policy allows images to be available to the public without legal penalization. These are free to be tattooed. However, photographs taken of these works are not public domain.
Logos which are trademarked may also be copyrighted. This adds another dimension of complexity to the copyright laws pertaining to tattoos. Sports logos are subject to both, since copyright does not cover company names or slogans, but protects artistic expression. Since most patrons do not profit off of tattooing a logo, and the artist is merely providing a service for private use, there is no trademark infringement. However, if you get an NFL logo tattoed without explicit permission from the NFL, you are violating copyright technically. A work-around can be uniquely incorporating a logo so that it merely looks inspired by an original design, but this is tricky.