You get collectibles by either a) going to the Shop tab & seeing what's there to buy (the stock will change every couple of months); b) get them from forum events like the Fair, Halloween, etc.; c) buying from other members
If you're looking to sell yours, go the TBT Marketplace and make a thread. You can see which collectibles you have in your inventory by going to Shop tab, then Inventory. If you're curious about their time-stamps then go to the Transaction Log in that same menu.
If you go to your collectible list, like Serena mentioned, you can see these buttons in the columns next to the names of the collectibles. Hit the "Gift" button, and put in the username you want the collectible to go to!