I went over the tooltips in the gameplay video to garner what information I could. The terrain and improvement yields appear to be mostly identical to current Civ V values. Keep in mind that these are early values and may change.
Grassland
Movement Cost: 1; Yield: 2 Food
Plains
Movement Cost: 1; Yield: 1 Food, 1 Production
Mountains
Notes: Impassable, provides science bonuses to adjacent Campus districts.
Hills
Movement Cost: 2; Defense Modifier: 3
Coast
Movement Cost: 1; Yield: 1 Gold, 1 Food
Woods
Movement Cost: 2; Defense Modifier: 3; Yield: 1 Food, 1 Production
Notes: Appear to give +1 Appeal to adjacent tiles.
Rain Forest
Notes: Provides minor science bonuses to adjacent Campus districts.
River
Notes: As before, rivers are positioned between tiles. Rivers appear to add +1 Appeal to adjacent tiles. Rivers now appear to require a certain number of movement points to cross, instead of just ending a unit's movement after crossing as in previous games.
Cliffs
Notes: Like rivers, cliffs can appear on the border between land and Coast tiles. Cliffs add to Appeal (likely +2).
Plantation
Yield: +1 Gold, +0.5 Housing
Farm
Yield: +1 Food +0.5 Housing
Camp
a tile with Deer, a Camp, and Woods yields 3 Food, 2 Production, and 1 Gold
Regarding districts, only the City Center and Holy Site were moused over. Note that both have Ancient Roads which provide 1 "Route Movement", and note also that the Holy Site district tile seems to only yield Faith, and not any Food from the grassland it's sitting on.
The tile with 7 Appeal is next to a Woods, a Cliff, and 2 x Barrier Reef natural wonder tiles; mostly likely +1 from Woods, +2 from Cliffs, and +2 Each from the natural wonder tiles.
I also noticed that the tiles being worked display: "Citizens working here: 1", implying that at some point it may be possible for more than 1 citizen to work a tile.