At which point in the ripening of the fruit are strawberry seeds ready to be harvested
For best results you should harvest the seeds when the fruit is fully ripe or starting to go a bit mushy.
how are they removed and cleaned?
There are several methods people use to remove them: scraping them off with knife or fingernails, mashing up the strawberry and straining the pulp for seeds or letting the strawberry dry out and scraping them off then.
Some just plant a squished overripe strawberry but I assume that removing the seeds leads to a higher percentage of them growing.
I personally don't know if one particular method leads to the best results but find that scraping them off gently is the easiest. If you wish you can then plant them straight away or clean and dry them for storage. If you are storing them you will need to make sure that they do not have any strawberry flesh stuck to them and are fully dry.
I have heard that if the seeds float they are not viable but do not know if this is true.
Do they need cold-stratification?
It is not necessary to treat the seeds with cold to get them to germinate but you can experiment to see if this speeds up the process. The general consensus seems to be that cold will increase the speed and success rate of the process.
How long do they store under good conditions?
I have successfully kept dried seeds for 6 months and been able to use them but I assume they can last longer than that as long as they are kept dry.
I assume berries picked green (such as many found in the grocery store) will have under-developed seeds, and poor germination. I have access to high quality, local fruit.
I have only ever used seeds from my own plants (originally from a garden center) but it's possible you can get viable seeds from some grocery fruit (Here they are picked when they are nearly ripe rather than green.) You may get varied results from these though as they could be hybrids.