To export a complete table, enter a table name in the table box or select one using the three dot chooser button. The table must be in the current database (the current database is green in the Entrance tree). Select an output format, click OK, and data will be epxorted.
To export a filtered table, open a table in Entrance, then enter a match pattern or WHERE clause in the match box. Now, when you open the export dialog, you will see a "Matching" message below the table name like the one above. Only matching rows will be exported. This feature works well with "data painting", which you will read about later: It makes it easy to export only the "blue" data points, for example.