I don't know if it's like this in other countries, but finding part time work in Barcelona is probably harder than landing a full time gig. Part of this has to do with the current economic environment, but mostly it's because the concept of flexible, part time jobs based on hourly wages, doesn't really exist here.
Sure, companies offer part time contracts, but they're usually for twenty-five hours a week, the choice of afternoon or evening shifts being your only option. You will be expected to work these set hours regardless of work load and sometimes more because there's no time sheet to monitor when you arrive and leave, and thus no overtime. To avoid paying summer vacation, employers will often only offer these contracts for periods of less than a year, say from September to June, so you'll be responsible for saving money from your 500-600 euro-a-month paycheck for a summer, winter vacations.
One of the problems I've had working on contracts, whether part time or full time, is that employers will often fiddle with the tax percentage, especially if you're hired during the year. This is often done without your knowledge and during the year it seems you're earning more, until April rolls around and you get a bill from the hacienda (tax department) saying you owe. Also switching jobs or going from part to full time or vice-versa will almost surely see you pay. It's almost enough to make a person decide never to file taxes ever again.
But if you're only planning on staying a short time, part time contracts do offer the chance of a steady income that will leave you free in the mornings or evenings. Most of the part time job market requires Spanish and is concentrated on sales, promotions. If you don't have knowledge of the language, there are call centers and English schools that offer part time work. The best place to find out if a place is hiring is through the Metropolitan Magazine available in many English pubs or on Loquo.
As I wrote in an earlier post, becoming an autónomo is also an option because it allows you to earn a decent hourly wage. But going through the process and paying the taxes really isn't worth it if you don't plan on staying for the long term. So what to do if you just want to earn enough to pay for your Barcelona adventure?
Personally, I think the best option is to go black. I mean economically speaking, not in the choice of your clothes' color. I think I read somewhere the underground economy constitutes a fifth of the Spanish GDP and there's a reason; it's the only way to make a decent living for many people.
Vast and covering almost every service sector, if you're fresh to the city and don't speak the language, there's the option of passing out fliers for one of the hundreds of bars competing for customers. I'm not sure how payment works, but people seem to get by and if often leads to other under the table promotional, bar work. Some restaurants might take you on and pay cash during peak months, as will smaller English schools but if all depends on how legal they are. If you like working with your hands, there is always boat work at the marina.
But in all honesty, I still think your best option for working part time is to discover you inner entrepreneur and do you own thing.