Okay, first I go to the folder that has the Atari 800 games. The games should have the extensions of either .atr .xex .cas or .bas. (.bas and .cas games will not appear in the Dingoo game menu). Select whatever game you want, and if the game doesn't start right away, but a blue screen appears instead asking for commands, press the left shoulder L button and the menu screen should appear. From there, go to Select System and make sure that Atari 800XL (64 kb) is highlighted. Then, after going back to the main menu, highlight Run Atari Program and press A. Use [..] to navigate to the games folder, highlight your game of choice and press A.
If that doesn't work, after pressing the left shoulder L button to activate the menu, highlight and select Cartridge Management, the highlight and select Remove Cartridge. I then highlight and select Disk Management. With D1 selected, I navigate to the games folder, highlight a game, press A, then press B when the Disk Management screen appears, and then B again at the main menu for the game to start.
IF THAT DOESN"T WORK (as in the case of Donkey Kong.atr), highlight and select Cartridge Management, highlight and select Remove Cartridge, go back to highlight and select Insert Cartridge. Highlight and select the game (DonkeyKong.atr for this situation) and the Select Cartridge Type screen appears. From there I highlight and select Standard 16 KB Cartridge and I'm brought back to the main menu. I press B and viola, it's on like Donkey Kong!
IF ALL THAT DOESN'T WORK (like with Cannon Duel.atr), THEN THE GAME MAY BE FAULTY.
As for the Atari 5200 games, make sure that you have the Atari 800 emulator already on. Go to Select System and then highlight and select Atari 5200 (16 KB). You should find yourself back in the main menu. From there, I go once more to Cartridge Management, highlight and select Remove Cartridge, then highlight and select Insert Cartridge. After navigating to the Atari 5200 game folder, highlight and select a game. Once you select a game, the Select Cartridge Type menu appears. From there you have to cycle thru the cartridge options until you find the right one. I usually go with Standard 8 KB 5200 Cartridge or One Chip 16 KB 5200 Cartridge. Once you press A to select the cartridge, you return to the main menu. Press B again and the game should start. If not, repeat until you find the right cartridge type.
I figured that all out through trial and error. If someone knows a better way, by all means let the Dingoo universe know.