I have some share/like buttons as well as my Google+ profile icon.
Is it correct to put them in the footer element at the bottom of my page?
The footer element is appropriate for such links.
It’s a pretty easy decision, as such links are clearly not part of a section’s main content, so there is only footer or header left as possible candidates. And here the definition of footer seems to come closer (emphasis mine):
[…] typically contains information about its section such as who wrote it, links to related documents, copyright data, and the like.
When the share/like links are for sharing/liking the article (e.g. in case of a blog post), use the footer of the article section.
When the share/like links are for sharing/liking the whole website, use the footer of the body sectioning root.
<body>
<article>
<footer><!-- for links applying to this article --></footer>
</article>
<footer><!-- for links applying to the whole page resp. site --></footer>
</body>
In case where the author of the article is a different person than the author of the page/website, place the profile links accordingly.
If the linked profile offers a way to contact you, you might use an address element in addition.
<footer>
<address><a>…</a></address>
</footer>
You may want to use the author resp. publisher link type.