Is 3 months a good length of notice to give?
Sure, but more importantly check what is the legal requirement for resigning from your position. For me it's 1 month, so I don't need to give any more heads-up, but it's surely appreciated. Consider that they will need to replace you with someone, which takes time to arrange.
When should I begin applying for positions in industry?
Today! Right this second.. No but seriously, depending on the type of job you are looking for, a good fit might not come around whenever. Keep an eye out there, have some job alerts for your favorite companies. Talk to people, reach out into your network.
A word of advice though, if you do reach out to your network and these people know your current employer, you want to make sure that your boss is aware you are looking for something. You don't want to leave the impression of going behind someones back.
I plan on leaving my current postdoc at the end of the first year to
go to industry.
1 year as a postdoc is hardly worth it though, the idea is to learn something new, to publish some articles, overall develop your skills. So, unless you are really tired of what you are doing I am not sure if a planned end by the first year makes any sense.