A 5 to 10 gallon aquarium or a container with a similar foot print could work as a culture vessile. You will want a container that is long and wide enough that the caulurpa is getting light evenly distributed over it. You must use salt water with an appropriate Specific gravity, the suggestion to use old water from your aquarium is a good idea, brand new, sterile water would not support macro algae very well. A lighting system with a kelvin temp in the 55K to 67K range is ideal, florescents such as PC work well but others have reported that grow light such as the type sold at hardware store work well. 12 + hour a day is typical but do not operate the lights 24 /7, Macro does better if it has a "night" cycle as well. A stagnant body of water is not ideal, you will want a small amount of gentle water current, a small power head should do the trick. I feel that a warmer, stable temperature is better than cooler, unregulated temp. You will see a more vigorus growth with a warmer temp (high70's to low 80's) A iron & magnesium supplement as well as a plant fertilizer can really make this stuff grow but use with caution, overdosing can cause unwanted algae (hair for example) and even can kill the caulerpa. Regular pruning of the caulerpa often prevents it from crashing and dying off. Some types aren't know for it (Grape for example) where as other are more prone to if (Taxifolia or floridea).
Hope this helps....Joel