A very good way to passively increase your stack of Bitcoins is through lending them out on an exchange like Poloniex. Traders who use margin can then borrow your bitcoins and pay you a fee. The first step is to sign up for an account at Poloniex and immediately begin the verification process by going to "My Profile" and entering in the requested information. Then you get your Bitcoin deposit address and use it to send some Bitcoin to your account. Don't have Bitcoin? Buy some at Coinbase.
Once the deposit clears, you need to move the funds from your "Exchange" account to your "Lending" account as shown below.
Then you simply click the "Lending" tab at the top, fill in your desired BTC amount, loan rate, duration, and choose if you want to Auto Renew.
Auto Renew simply means that when the loan expires, the system will automatically put a new loan offer out at the same rate. The loan can expire at any time up to the duration you selected, depending on if the trader who took your loan closes out their position or not.
Automated Lending with Polobot
In order to take this to the next level, you need to use a lending bot. With rates constantly changing, you can't rely on auto renew to keep your coins loaned out at the best rate. I have used PoloBot for several months now and highly recommend their service. Simply sign up for their service then under "My Account" be sure to link an API key and secret that you can create in your Poloniex account.
If you have a good amount of bitcoins, you should strongly consider becoming a premium member for a donation of 0.05 BTC. This will change the bot to update new loan offers every 5 minutes instead of every four hours. You'll also need to create a bot for each cryptocurrency you'd like to lend out on Poloniex. These are my current settings for my BTC lending bot.
Once you've done all of this, you should be ready to start letting your bitcoin work for you. There are additional instructions on www.polobot.net if you have any issues setting it up. The creator is very active in the forum as well as on reddit if you have any questions. Right now rates are very low as you can see, but from time to time they do increase so it's worth it to have this set up and ready to go when the opportunity presents itself. If you have any questions or comments I will be happy to answer them.