Nominal data analysis generally involves the categorization of information into helpful sets. Pieces of data may or may not have numerals (numbers used as symbols) used to identify them (think of a number on an assigned parking space), but they are not used for counting purposes--just classification. Examples might include a list of soft drinks with caffeine, or the jersey numbers of baseball players with starting pitching experience.
Ordinal data analysis takes the results of nominal analysis and provides a ranking of some sort. This could be chronological order, order of authority, and so on. If you take the examples from the nominal analysis section, you could rank the sodas from highest to lowest caffeine content, or you could rank the pitchers from highest to lowest in terms of games won.
While not all data sets can employ interval analysis, this can be a particularly helpful tool for giving subjective responses a quantifiable identity. Attitudinal scales are a popular example of this for psychological studies, involving questions where the respondent is given a statement and asked to strongly disagree, disagree, slightly disagree, be neutral, slightly agree, agree or strongly disagree. Each response is equated with a number (here, one through seven), and those numbers are averaged to give quantifiable results.
With ratio analysis, respondents are also compared to one another. While interval data just measures one person or measurement at a time, ratio data could appear on a real number line with a real zero. For example, if the study is looking at weight loss over time for a group of 50 people, comparing their net weight loss and percentage weight loss against each other over time would be an example of ratio-based analysis.