The ATtiny85 can be used to create small and compact circuits. The ATtiny85 can be programmed by a microcontroller, for example an Arduino Uno as ISP or with an USBasp AVR Programmer.
While the ATtiny85 has only 6 functional pins, it is still quite powerful. With (software) I2C, SPI, UART or default input/output a lot can be achieved. (Especially when multiple I2C devices are used).
The ATtiny85 can run on the internal 8MHZ oscillator which is more than enough for most applications.
See the following video for instructions: Programming an ATtiny85/45 with an Arduino UNO
See the datasheet under the tab “Downloads” for more information.