You can’t get in much trouble for non-commercial use of copyrighted work that YOU perform. That is, if you re-draw, re-paint, reproduce a photograph, etc. – or cover a song that someone else wrote or sang, or copy a sculpture or even rewrite a copyrighted narrative work – AND if you don’t use it in furtherance of some other commercial endeavor (like singing “Happy Birthday” – one of the most aggressively defended copyrighted works in our culture – at a restaurant, for example), then there’s generally no trouble.
That’s why we can all sing Happy Birthday to You at private parties without giving it a thought: there’s no commercial aspect of that. No one will sue you for singing that song at your friend’s or family’s birthday parties. But when it is sung in a restaurant, or by a caterer, or by a professional singer who is being paid – then the copyright is enforced and protected, and a license (usually paid for) is required.
So you can copy someone else’s work for your own private, non-commercial enjoyment. (This generally also applies to literary or artistic criticism or review, and also – in general – for scholarship purposes.)
When you “put it on the Web” then it can become dicier. For example, if you put it on your own Photobucket, or Facebook or Tumblr page or some others where the image itself isn’t driving traffic to an advertiser or linked to a product for sale (or the web page itself isn’t “by paid subscription”) then you’re probably okay. (The qualification is because all of those services do sell ads, and they themselves might demand that you remove the work in question if there is any question about whether you’re attempting a work of homage, fair use or commentary – or trying to pass off the work as “your original creation”. Or if the original license holder objects, obviously.)
If the presentation is on a page that is “yours alone” and you have no avenue or vehicle or intent to profit from the image (and if you are not, in fact, profiting “despite your stated intent”), then it’s more certain that you can do as you like. In those cases, again, the reproduction isn’t even visible to most internet users (or to the license holder) and there can be no objection because of the general privacy of the thing. (That’s “in general”, because even private pages can be viewed or hacked by those, and then become public.)
Generally, though, when these questions arise and there is no clear profit motive (or profits), no flagrant attempt to pass the work off as one’s own, and when the original copyright holder objects, then you (or the web page owner or service) will be contacted by the holder’s agent (usually an attorney) with a “cease and desist order” – which may contain the threat of a complaint and unspecified future legal action – but no one wants to pay money to prosecute those cases when there’s no money to be recovered. They just want the perceived abuse to stop, and to protect their valid copyright.
On the other hand – or maybe “the other other hand” by now – imperfect reproductions such as an amateur singer attempting to cover a song, or your hand drawing of someone else’s photograph or other work of that nature, and presented respectfully or as clear parody or review / commentary will generally be considered “fair use” and ignored.
There is no question of “illegality” here. No one is going to arrest you for non-financial reproduction or copying in this way. If you ignore a valid C&D letter, then the copyright holder may follow through on the threat, however.
The best advice is not to copy too closely or too deliberately, certainly to ensure that there is no money changing hands or being requested, to credit the original artist in your reproduction, and to make sure that there’s no prohibited future use of the work.
If you really want to be certain, then you can contact the agent for the artist up front and request a license to reproduce, display, perform, exhibit or post your work. “Reprinted with permission” is always the most respectful form of homage.