Anne has given the standard advice for choke growing, while this is very sound advice it may help to know how these are grown in Castroville, CA. "The artichoke capitol of the world".
The soil in Castroville is rich loam and close
enough to the sea that there is always some breeze and evening fogs roll in regularly. In this location the plants are
perennial and produce for about 7 years before they are pulled and replaced.
The early start mentioned by Anne is one of the keys to growing good new artichoke plants. If you don't want to start them indoors or in a green house then you will need (or want) heavy row covers to hold in the suns heat while starting the seeds in late January or early February.
Starting them under row covers eliminates the need for hardening off, since they are already in their home spot. On warmer days after they have sprouted you can lift the cover sides up for better air circulation.
The best soil for artichokes is very deep (1.5 feet), humus rich (25%), well draining (sandy) top soil.
One of the best types of fertilizer's for artichokes is also for tomatoes, if you are going to use a commercial type of fertilizer that is.
Soil that has been amended with good compost and well composted cow manure or sheep manure will produce near perfect plants that will produce quite well.
If you notice yellowing tips of the leaves then an addition of green sand or kelp will be beneficial to the production rate. Artichoke plants will normally produce at least 5 flowers per season.
If you have winter weather temps near 35 f. then you will need to use a blanket cover to protect them from frost kill.
This is one plant that tolerates slightly salty soils so you could give them a watering of sea water ( a good, mineral rich, sea salt dissolved at 2 TBS per gal. once a month will not hurt them and will give them better flavor)
Artichokes do best when spaced 3 ft. to 4 ft. apart, these plants tend to not do well if crowded, they need air flowing around them.