The source text and the target text are displayed next to each other in the top-middle. Between them you can see a column with the segment statuses which will change as you work on and confirm segments. You can hover over the icons to see what they are, and you can find full details on this Across online help page under Paragraph states.
Any locked segments have a grey background and they cannot be edited. Editable segments will have a white background.
Type in your translation in the target editor. Confirm the segment to their final paragraph state (this is usually Translated for translation tasks, Corrected for correction tasks etc) and move to the next segment. If you start typing a translation and move to the next segment before you confirm it, it will be left with the status Touched (or, if you are working on a revision, its existing Translated status) and not stored in the TM.
Note that auto-propagation propagates all identical segments, but marks them as Touched unless you configure them to propagate the paragraph status as well as the actual translation in Tools > User Settings > crossDesk > Auto-propagate.
To ensure optimal leverage during translation: Confirm to their final paragraph state as you go through them rather than leaving them as Touched or whatever their existing state is. By doing this you will get the full "fuzzy match" benefit from your own work as you go along, not just the fuzzies already present in the client TM at the start of the project. Confirming segments to their final paragraph state writes new records to the crossTank TM. As long as you do NOT finish and deliver the task, records from one task will also appear for the next task because they are still in the local tank. This is a useful hint for small projects with repetition between them if they have the same due date. However, never delay a delivery past its deadline just to keep the crossTank populated.