In match reports, you can see what events happened in a particular match. All scoring opportunities, injuries and cards are reported here. Possession percentages, Tactics ratings and sector ratings for both teams appear when the match is finished.
If you click on player ratings under a team name at the right, you can see how well each player played in that match, shown in stars. If the match is ongoing, the ratings will be absent, and only the events that have happened so far are displayed. Those watching their matches on HT-Live (Link) will see the latest events appear roughly minute-by-minute in red text. Many players love almost nothing as much as the appearance of new 'red text':)
There are a number of other ways to 'watch' your match(es) live. These are being improved by volunteer programmers regularly.
Bear in mind that for the first 5-10minutes of a live game no information will arrive, which is normal.