Gallup publishes the data along with the methodology:
Results are based on telephone interviews conducted May 3-6, 2012 with a random sample of –1,024—adults, aged 18+, living in all 50 U.S. states and the District of Columbia.
For results based on the total sample of national adults, one can say with 95% confidence that the margin of error is ±4 percentage points.
For results based on the sample of –534—national adults in Form A and –490—national adults in Form B, the maximum margins of sampling error are ±5 percentage points.
Interviews are conducted with respondents on landline telephones and cellular phones, with interviews conducted in Spanish for respondents who are primarily Spanish-speaking. Each sample includes a minimum quota of 400 cell phone respondents and 600 landline respondents, with additional minimum quotas among landline respondents by region. Landline numbers are chosen at random among listed telephone numbers, cell phone numbers are selected using random-digit dial methods. Landline respondents are chosen at random within each household on the basis of which member had the most recent birthday.
Samples are weighted by gender, age, race, Hispanic ethnicity, education, region, adults in the household, and phone status (cell phone only/landline only/both, having an unlisted landline number, and being cell phone mostly). Demographic weighting targets are based on the March 2011 Current Population Survey figures for the age 18+ non-institutionalized population living in U.S. telephone households. All reported margins of sampling error include the computed design effects for weighting and sample design.
In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.
So in other words there's about a 5-point margin of error on the results, and they may well be imprecise due to lying.
In other words, the results are way less precise than presented. It is assumed that there will be errors, but that the picture is substantially correct. I find no fault in the overall picture, but of course the exact numbers are probably different from what was presented.
In any case, what counts is the qualitative answer: most US residents are creationists. Quantitatively we can say it's the largest subset, although the number is only known to be between 41 and 51 percent of the population (within a 2σ — 95% — confidence interval)
Furthermore, the results are slightly different from what is presented on the main site, from the same pdf as above:
From the table above it is clear that, once we consider the 5 point uncertainty, nothing new has emerged from the poll: the fluctuations of the values across the years are consistent with the predicted errors.
Finally, there's a big manipulation here: the significant question is whether man evolved or not, not whether God assisted! Believing that God influences the world has nothing to do with either the scientific position of evolution and the charlatanerie of creationism.
If one discards that false dilemma, then the numbers look much more sane and believable: 47% of Americans accept evolution, and 46% believe in the superstition of creationism. It's still a frighteningly high percentage though.
The polls don't account directly for people being dishonest. However, that's not the big problem. The real sham is the misrepresentation of the results via omitting the error bars and introducing a false dilemma to make the position of evolution look much, much lower than it is.