If the person's last name is Smiths, with the S at the end, it would be Mr. Smiths's office. If the person's last name is Smith, it would be Mr. Smith's office.
Here's all you need to know about apostrophe use:
1) You ALWAYS use an apostrophe to show a possessive (who owns something). It is never correct to leave off an apostrophe in a possessive, with the single exception of the word "its," as in "the dog wagged its tail."
Also the other possessive pronouns, including hers, ours, yours, theirs, his. Yeah, "hi's" will really make a writer look less-than-knowledgeable.
2) You NEVER use an apostrophe to show a plural (when a noun refers to more than one.) It is always "there are lots of girls at the school," NEVER "there are lots of girl's at the school."
3) It is always correct to use an apostrophe to indicate a contraction (the merging of two words into one). "There's" is the contraction for "there is." "What's" is the contraction for "what is." "It's" is the contraction for "it is."
Yep. Worse to my old eyes is: I lived through the 60's. Instead of indicating where 19 is missing by the proper apostrophe, many writers misplace it to confuse the plural.
That's it! That's all you need to know about apostrophes. They're pretty simple to master.