Determine if the samples are matched-pairs. Studies usually list how the data was gathered in a methodology section. You can identify matched-pairs if the measurements on the subjects were related to each other. For example, say you have several containers of water and you tested each sample for temperature and dissolved carbon dioxide. These samples (temperature and dissolved carbon dioxide) would be matched-pairs since temperature affects dissolved carbon dioxide in water.
Determine if the samples are repeated measures. An experimental design using repeated measures tests the same subjects more than once. A pretest followed by a post-test is a good example. Repeated measures are used when it is not possible to separate the subjects into experimental and control groups.
Try to correlate the data in the two samples. A common test for this is the Pearson Product Moment Coefficient (denoted by "r"). If the data show a correlation, then the samples should be considered dependent. If the value of r is inconclusive (r = .2 for example), then you may need to make a decision about whether to classify the samples as independent or dependent. Whichever you chose, report your reasoning and the value of r in your report.