An earth type planet as the moon of a Jupiter sized planet would proably rotate with one side facing the planet, as our moon does, or Venus. It is possible to have life, but it would not be a greate climate.
If the gas giant was several times more massive than Jupiter then the Earth like planet would zoom around it close to what we have now. You'd might have a longer day & night but it shouldn't be that bad.
Now if the Gas Giant was about the same size as Jupiter, day and night might last a week or two each. That would be extreme as you would essentially go through all four seasons in one day. Spring in the morning, summer in the afternoon, fall in the evening and winter at night.
And that's only if the gas giant and the earth like planet are like Jupiter and have a insignificant axis tilt, if the gas giant and/or the earth like planet was tilted like earth you'd get seasons within seasons, 4 yearly seasons to go with your 4 daily seasons.