After a match, you see the Match Stats interface, which tells you the K/D/A, XPPM, GPM, APM, and item builds of all players. It also has "View Stats" and "Add Buddy" buttons for each player.
The "View Stats" button takes you to that player's overall stats page. It should instead give detailed stats for that player for that specific game. This would include ability build, item purchase times, wards bought, total damage to enemy heroes, total damage to buildings, and K/D/A on each enemy hero. It would also tell you the total amount of gold the player gained that game, and how much of that earning came from creep kills (including Alchemist's Bones), neutral kills (including Kongor), building kills (including "team gold" from buildings), hero kills, hero assists, and passive gold. Basically, it would be a more detailed version of what you see when you click on the "Details" button on the website's Match Stats page.