Left box is where you select the character to be buffed, while the right is where you select the sacrifices.
The red box shows the cost needed vs your available gold. Select the main card, then tap the area on the right to select the sacrifices.
You can select up to 10 cards per synthesis. Deselect a selected card with the grey box similar to what you've done in the party setup. Note that you won't be able to select locked cards in this process. Press the gold OK button and.......
Back to the synthesis screen we go. If you've feed a weapon, then the 武器進化 icon will show up. And if you've feed a weapon upgrade card, the 武器強化 icon will appear with the success rate for weapon growth. If you're feeding only experience cards for the character, none of the above two mentioned icon will appear. Press the red はずす icon to remove the selected sacrifice, and the blue item will perform the synthesis.
The 売卻 hexagon icon will bring you to the selling screen.
And the selling screen. Nothing way too different, except you get to see something new in the form of a ring. It's another form of currency in the game, which can be used to exchange stuff, including the SSRs of the month. Press the 売卻 blue icon to confirm the sale.