There are 2 types of applications you'll download from above links. For desktops, you'll download Mavis Hub, the launcher for Axie Infinity games. Whereas for mobiles, you'll directly download the game app.
After installing and launching Mavis Hub, you first need to login using your email and password.
Once you're logged in, you'll see the PLAY button, which you can now click to start your game! (You'll be prompted to install the game on the first launch)
To login on mobile devices, you'll need a QR code
To get a QR code simply go to https://marketplace.axieinfinity.com/profile/dashboard, login with your credentials and you'll see the "Show QR" button.
Another option is if you have Mavis Hub installed, you can click on the cog icon beside your user name. Next, click on "Show QR code" on the pop-up. You'll be presented with the QR you need to scan from your mobile device.
You can see your axies on the marketplace: https://marketplace.axieinfinity.com/profile/inventory/axie
You need to sync your axies first thing in the game.