Start with a strong website with good pictures and specialties. Make sure your website is search engine optimized. Get a Yelp profile going. Might want to try Google adwords. Consider ways to market yourself to your clientele. Who's your customer base? Are you open to the public or b2b?
Then I would start putting some fun creative stuff on Facebook and Snapchat. Like videos of you baking something that looks good. Start searching twitter hashtags concerning food, baked goods, sweet treats, etc. read in on the conversations and engage with people. Follow them and hopefully follow them back. Start tweeting Picts of the daily specials, always linking back to the website. Also on social push the specialty items. Christmas cookies and cakes, Halloween treats, Easter, valentines days, Jewish treats and traditional foods.
For bigger budget consider a tv schedule to unveil your brand. Is it fresh? Healthy? Wholesome? Decadent? Etc. perhaps a promotional offers, like half dozen sugar cookies with $20 order or something like that.
Finally send free samples to the morning shows of local tv and radio. Maybe they'd have you on? People in broadcasting love free food. Maybe you would get a mention?
The rest is hardwork and word of mouth. Because no amount of advertising can sell a bad product well over time. The best businesses especially with food seem to do amazingly well if they have a product people crave.
I agree with Charles regarding sending free samples to local tv and radio...this almost always does the trick. Coupons and sampling are also effective ways of driving traffic to your store. A sampling of your product is most important so you'll want to get your customers to try it. Consider large events in the town where you plan on opening the bakery and, either provide the product to taste or a coupon for a free taste.
As mentioned word of mouth is the best form of advertising and is free, but you have to give them something to talk about. Good luck!
Great recommendations so far and I agree with all of them. This sounds like an exciting school project. In addition to working with social media bloggers and vloggers I would also recommend you setup your own Instagram, Facebook and Pinterest pages as well to feature your work. This can be done through videos showing how your baked goods are made. Provide fun tips and hints for party ideas and maybe host a cooking class or two. All of this goes a long way in building your exposure and good will with potential customers. They can also be great things to mention to other bloggers, vloggers, TV and Radio Stations to build awareness. Best of luck!
First of all it's great that you are getting this kind of experience as part of the school project. Below is what I would suggest for marketing.
1) Build a website - You can use google site, wix.com for free website templates. You just need to come up with content. You can use fiverr.com to hire someone for nominal cost to write content for the website too.
2) Digital Marketing Options - Digital marketing is one of the most effective way because costs are low and ROI (Return on investment) can be tracked properly. I would suggest you open up a business page on Facebook. Use that page to market your newest creation. Your sale etc. Then I would suggest using Google Ad words to do some search engine marketing for people who are looking for cupcakes in their area. I would suggest targeting your immediate geographical location (city or few zip codes) to keep cost low and ad relevant. You can use extensions like phone number, maps etc to drive people to your location or call your drive them to your website.
3) Yelp - I agree with what has been said that you should create Yelp account but also google business page as well. This will make you show up on google organic search as well.
4) Business Connections - I would go up to few businesses in your area and work with receptionist or office manager to deliver cupcakes at a discount.
5) Evite - You can use Evite.com to advertise to people who have specific parties like birthday parties and drive them to your site. (This is a bit more expensive but you can replicate that in google ad words and facebook using behavioral, age, and life events categories for targeting.
Hope this helps.