Apply to every firm advertising vacancies and make sure you don't take any unpaid gigs.

Apply to as many as you can within your maximum commuting range. Many will never respond back. A lot of firms do not have applications but I would find a specific person to contact. or call and ask for a specific email. (Those online information request fields that a lot have are useless) 

In my experience, I sent out tons of emails as a second year not expecting anything and I found that asking for an internship outside of bigger cities the firms were a lot more likely to get back with me on the possibility. The areas where arch schools are were less likely to be hiring. I ended up getting two internships opportunities near my hometown for the summers. The firms had NEVER had an intern. They had never had a request for an intern even. While many of my friends who remained at school for the summer could never find one.(Located in the largest city of our state). 

They were small, not glamorous, and not staritecture offices but they were valuable and I was able to have a take away and save lots of money on rent and such. 

Personally, I wouldn't just show up at a firm with my resume/portfolio in hand knowing how crazy it was at my own internship. 

Always make sure it is paid

goodluck!

the first time i applied for internships, i looked for job postings and submitted an application.  ~80 applications, zero callbacks.  super demoralizing. 

the next time around, i found alumni at offices i was interested in, did an informational interview (usually email), and they passed along my portfolio.  much fewer applications this way, but 10 for 10 offered positions.   

my experience backs up that old chestnut "it's not what you know, but who you know".  use your network to get an internship, don't rely on HR processes via. the black hole of online application portals.  

I worked three internships before I got hired in a long-term position.  All three I found through my university.  Employers would often email the head of our department looking for students to intern and periodically the dept head would forward them along to everyone.  In my case, all three of the places I went had established internship programs.  However, there are plenty of offices that do not (my current office included) but would love to have someone help out for a bit that is interested and wants to learn.  

I did 2 internships back in uni, one was through my father's friend and that was during my second year of university, and the second was through an organization i was a part of - fourth year. 

Try to see if you know someone that can hook you up with an interview at least (family, friends, professors) and also check the career department at your university. 

At the time, I never applied to hundreds of firms at a time because I usually don't believe that's a good strategy. HOWEVER, that's how I landed my current job after uni. So it could go either way, but I do recommend knowing who you're contacting and not just sending emails to "info@firm.com" 

Goodluck!

Have to agree with most points made above. In my experience it is Key to write a cover letter that specifically addresses why the firm is right for you, and why you are right for the firm. They will be much more likely to write back to someone they already feel akin to. 

Another key is to find people (former classmates, professors, family friends) in the industry and reach out to them. As stated above, knowing someone at a firm multiplies your chances. I can speak to this from experience - I got an internship at a global design firm through one of my critique jury members, and I now work full time here. I have been able to recommend former classmates of mine as interns and pass along the torch.