Do it like she does. Sentences like that one have always been unacceptable to purists. Nowadays, however, such sentences go virtually unchallenged, even by many editors.
Traditionally, like can only be a preposition meaning "similar to" or "similarly to." So Do it like her (i.e., similarly to her) would be correct. But because no one would say, "Do it similarly to she does," there is no grammatical justification for Do it like she does.
In the mid-twentieth century, Theodore M. Bernstein said in The Careful Writer: "The usage of like as a conjunction…is not acceptable in better-grade writing."
The American Heritage Dictionary's panel of experts has noted that for more than a century, anyone who said like she does was considered illiterate. Yet today, the panel says, "Like is more acceptably used as a conjunction in informal style."
The traditional view is that if a verb follows the noun or pronoun, as in like she does, it means like is the wrong choice. Instead, use as, as if, as though, or the way.