We only spent two days in Delft, and since the weather was particularly bad that weekend (incredibly windy both days with rain on the first), we didn't get to see what is probably the most popular attraction - the Porcelijn Fabriek (the Porcelain Factory).
We did walk around the local outdoor market, which, despite the weather, was wonderful! Lots of small fruit, vegetable, cheese, meat, fish and sweets vendors. Our favorite was the "Stroopwafel" vendor. Stroopwafels are a popular Dutch treat, usually eaten with coffee. They're round thin waffels with a sweet syrup in the middle. The vendor gave us one from his latest batch, and it was the best one I've ever had! (And I've sampled a few. . .)
Quick Tips:
Don't count on doing a lot of activities on Sundays. Almost every shop is closed, and only a couple museums are open for the afternoon. The Porcelain Factory is NOT open on Sundays. (We learned this the hard way.)
We did, however, buy a beautiful hand-painted Dutch tile from the late 1700s at a local antique shop called the Porcelijne Lampetkan, located near the Nieuwe Kerk. I would highly recommend visiting this store. Most of the items are antique pieces of Delft and antique maps, but we were thrilled to find such a lovely souvenir for only 30 Euros.
Best Way To Get Around:
We took the train from Amsterdam to Delft directly. It's only an hour and quite efficient and inexpensive. No connections necessary.
Once we arrived in Delft, we walked everywhere. It wasn't until we were leaving that I realized Delft even had a tram system. It's nothing like Amsterdam's however. It doesn't run through the center of the town - I imagine it just loops around it. Probably helpful in getting you from the train station to the popular Porcelain Factory though.
We found it very easy to walk everywhere in Delft - even with the bad weather.