We are a huge pin trading family. Well, DW is a huge pin trader, the rest of the family just dabble in it really. I have maybe 50-75 pins. DW has well over 1000 in her collection (maybe several thousand? I don't count anymore).
The EASIEST way to start is to just buy one of the starter sets at any park. This will include a lanyard and 6-10 pins depending on the set. Then start trading with the cast members. Note that you can also trade with other pin trader guests in the parks. Interesting that last trip we did a whole bunch of trading with other guests, and it was really fun spreading a little pixie dust as I just gave a few pins out to the younger kids just starting out.
Now the CHEAPEST way to get started is to buy a bulk pack of pins on eBay. We usually order about 75 pins from a reputable seller before a trip. We'll keep some that we want, but most are set aside for trading. I'll fill a lanyard in the morning, and trade them away through the day. DW usually brings two lanyards, plus spares to swap in. You can use any lanyard, but Disney does have some really cool ones. Pretty sure all of our lanyards are authentic Disney.
Note that in these bulk packs you will likely get a few of what are called "scrappers"; these are actually fake pins, but not of too much concern. Disney CM's and most traders can't tell the difference, so a lot of the pins you trade with CM's will be fakes as well. It is cause of great argument between the hard-core traders if a pin is fake or not, but we trade for the fun and sport of it, and don't really care if a pin is legitimate unless we are trying to collect a full set of specifically legitimate pins. It just adds to the chase trying to get the legitimate ones.
7 months is probably too young to really get it. Older kids can try to collect sets, or pick a favorite character and collect those pins. I'm a Goofy collector personally.
Check out the official Disney Pin Trading Etiquette to understand "the rules".
http://www.disneyparksmerchandise.com/parksauthentic/disney-pin-trading-guidelines-for-guests/
There is also a Canadian Pin Traders group on Facebook if you are a member.