Yes, GND to GND. For Vcc, 3,3 or 5 Volt, check the specifilation for that board. It might be possible that the BME 280 wants 3,3 Volt supply, and logic. In that case You need a level shifter, 5.0 to 3,3 volt between the UNO and the BME 280.
The UNO has a 3,3 supply to use but check the logoc level. The UNO uses 5.0 Volt.
An UNO usually have the SCL and SDA on the edge of the long connector, near the reset button and the USB connector. Look at the back side of the UNO if You don't find it on the front side. Also a pair of the analog inputs work, A0/A1 if I'm right.
Seems that module has a 3.3volt regulator, level shifter, and 10k pull up mounted on the back.
Always better to post a weblink to the part, instead of just a picture.
If it's what I think it is, then the module can be powered from 5volt, and connected directly to the SCL/SDA pins of the Uno.
Leo..
@Wawa
Where did You find that spec? I have tried. I have one board with 6 connectors, running both SPI and I2C, and it is the 3.3 volt version.
I have ordered but not yet received a 4 connector board that I hope runs from 5 volt, equipped with the level shifter.
Sorry for interviening, hope it will spread some knowledge to Forum members.