AVR chips will have their IO pins default to Digital I/O inputs on startup. All "alternate functions" will be inactive, meaning that the pins will just be digital input GPIOS until you activate a component that requires one of the pins.
For example, if you want to use the ADC on the ATTiny85, you write 0x80 to the register ADCSRA to enable it (that places a "1" in the enable bit of the ADC control register). When you do that, the ADC controller will essentially take over the pins it needs and configure them as needed. Depending on your ADC configuration, it may take over several pins. Let's say you're using an external voltage reference for your ADC, which is on pin PB0. At this point, PB0 can no longer be used as a digital input pin because the alternate function is active, and pins can only do one thing at a time.
As Ignacio mentioned in his answer, you can always read/write from/to the pins regardless of the function selected, but you are likely to interfere with the operation of whatever is using that pin.
Now let's say I want to use an external interrupt. I will have to choose one besides PCINT0, because that interrupt also uses PB0, which is already taken by my ADC. There is no "priority" - alternate functions will interfere with each other if you try to enable multiple peripherals that use the same pins.
Now, if I go disable the ADC, then the pins it used are free again. I don't think the pins will be returned to their previous states, so if you want to use them as digital input again, I would write to the necessary registers first to confirm they are in that mode.