Obviously you can't make a blanket statement about all artisans everywhere at all times. Just one piece of the puzzle will do nicely.
What time period, region, and culture are you asking about? Answers will be different if you're asking about the Nuragic people of Sardinia, Han China, or colonial Peru for example.
/u/Mictlantecuhtli is absolutely correct that the answer to this question is going to depend very heavily on the when and where for a detailed answer. However, I can try and answer your question by going over some of the factors to consider in talking about artisans in a particular society.
First of all, by "Artisan" I assume you mean any sort of craft specialist - as person whose primary profession is to produce certain types of goods.
In archaeology at least, craft specialists are grouped into two rough categories: "attached" specialists and "independent" specialists.
Attached specialists are given patronage to produce for a specific individual or group, usually elites. These would be your Michelangelos and Donatellos or your Shang bronzeworkers producing bronze vessels for state and funerary rituals.
The items produce by attached specialists are of course going to reflect their patron's desires, but to what degree very much depends on the patron and the society. The patronage relationships is such that the specialist doesn't need to supply for their own livelihood. The elite patron uses some of the surplus they gather as part of their social status, whether taxes in coinage, food, or other goods, to support the livelihood of their attached specialists.
Independent specialists on the other hand produce items as they see fit, but they are dependent for their livelihood on exchanging or selling their goods for necessities.
One example would be Hohokam potters in the Phoenix basin, where certain villages would specialize in producing pottery that would be traded to non-pottery producing villages, likely for food to supplement what was produced by the smaller population of farmers at these specialist village.
The kinds of items independent specialists produce are more regulated by market factors than attached specialists who always have a relatively fixed supply and demand structure. Again, the amount to which this is true is very dependent on the when and where.
Of course, a society can have both independent and attached specialists and a single individual could work as both an independent and attached specialist at different times.
One very general distinction between attached and independent specialists (though again, very much dependent on when and where) is that attached specialists are generally producing prestige goods, such as jewelry or other artwork, whereas independent specialists are producing utilitarian or every day items, such as cooking vessels or work clothing. Again, this is a very general distinction that is highly contingent on the culture in question, but is something to help structure how you think about craft specialists.
A final consideration in regards to your question about their social and economic status. This again is highly variable, and I hesitate to use the terminology like "middle class" in relation to many times and cultures, but there I can give at least one example of a case where craft specialists are not strictly middle or lower class individuals.
The Classic Maya are an excellent example where it was in fact the elite who were the primary craft specialists when it came to prestige goods such as painting, sculpture, and writing. The specialized knowledge required to produce these works was considered the appropriate domain of the elite, and likely the younger sons of Maya nobles would train to work as scribes, sculptors, or painters. Noble women may have worked to produce luxury textiles.
Again, the answer to this question is highly variable depending on the society in question, but I hope this gives at least some idea about the relevant angles to approach the topic from as well as giving an impression of the great diversity of craft specialists across different societies.
Sources: