How do I know if I have patentable features or functionality in my software?

Good questions. Software is generally protected with copyright, not patents. If your code has been cut and pasted from others code, that may be copyright infringement on your part. You should meet with a local Intellectual Property lawyer/fim and discuss your situation. Good luck.

Although it has become much harder to patent software in light of recent Supreme Court decisions, it is not impossible. The only way to know if you poitentially have something patentable is to engage a patent attorney, have a search done, and rely upon their expertise to evaluate the search results.
As far as stepping on someone else's IP, you would need to do a patent clearance search. You should talk about that with a patent attorney as well, although typically, for a web type application, I am not sure the cost merits such a search.
You will also probably want to do a trademark clearance for the name and/or any tag line that you may use with your application to make sure that you don't launch only to get a cease and desist letter because someone has a registered trademark that you are infringing.
As to copyright, if you independently developed the code from scratch, you should have nothing to worry about. However, if you based your code on, or incorporated, the code of others, then you should discuss that with an attorney as well. Even if you used open source code subject to one of the open source licenses (like the GPL), you need to ensure that you have complied with the license requirements. An IP attorney experienced with those licenses can help you there.
Note, the above does not necessarily require you to engage several different attorneys. Many of us have experience (personally or within the same firm) across all of the areas.
Good luck!

The best way to find out if you have any claims that may qualify for a patent is to talk to a patent attorney. Having someone look at your software before you launch is the best way to find out whether you are risking infringing any existing patents. Talk to a qualified patent attorney in private and get some advice. It's cheaper than defending a claim you've infringed someone's existing patent. Best of luck!

Although I agree with the comments of all my colleagues below, some of the more detailed thoughts laid out by Attorney Straussman are particularly helpful for you. Yes, many of us do indeed have the broad ability to help you in many of these areas or we work for a firm that could handle all of these areas. However, I think it makes sense for you to work with a firm that could perhaps cover these areas and more. For those reasons, you will probably want to work with a local firm and in particular, an attorney licensed in your state of Washington. I think this is important for you because there are numerous cross-over business and intellectual property issues, some of which are covered by Federal Law and others by State law. Some other issues for you to consider in this regard, you may wish to create a legal entity, i.e. company, from which to do business and perhaps look for some outside funding from investors. These issues require a knowledgeable business law or corporate attorney to help you, maybe even one familiar with securities law issues. If you are using ANY third party developers, you definitely need an experienced lawyer to advise you how to structure independent contractor agreements to help you protect your IP. You might have subject matter better suited to protection under trade secret law, rather than patents. If so, TS is a state law issue requiring someone familiar with WA state laws in this area. With respect to copyright of software code that is also a trade secret, there are some specific ways to go about this at the Copyright Office. To claim trade secret protection under your own state law or other state laws, there are very specific steps that must be followed to protect it. Lastly, the code you have used MUST have been independently developed and not developed by someone who had access to similar code. If that turned out to be the case, you could have BIG problems. What I am getting at is all of this is extremely expensive from having the necessary legal work done at a high quality. You need to think of your business in the context of a business plan taking into account all of the true costs of the business. I have outlined many of the legal ones but you will have many more in non-legal areas. Good luck to you but go into this with your eyes open about how much investment is required and what kind of revenue potential exists!!

In order to know if you have something patentable and if you might infringe on someone's else's IP you need to consult with an experienced Patent/IP attorney. Besides patent protection, you can also register a copyright on your web app. I suggest that you contact an experienced patent /IP attorney that can advise you in confidence. Many Patent /IP firms, like our own, offer an initial free conference by telephone, video conference or in person if you are available locally and would be happy to speak with you. Call and speak with an experienced Patent/IP attorney who can assist you.

This is not an easy question for reasons that are briefly touched on in other posts.
The problem stems from the Supreme Court's ruling in the case Alice Corp v. CLS Bank International (you should Google the case and read it and the myriad of comments about it). The Court ruled that Alice Corp's patent claims were invalid (the patent was improperly granted) because they were not patentable subject matter as defined by 35 USC 101. The problem was that Alice Corp's patent simply used the computer to do something faster (mortgage calculations) that could already be done.
There are other problems with the case as well (as the saying goes, a bad case makes for bad law) and many lawyers have been calling for a better case to make it up to the Court to get the problem resolved.
Since Alice Corp, the Federal Courts have been invalidating patents - especially those involving software and business methods - at an alarming clip. And, the USPTO is issuing rejections of applications under Section 101 at an even higher rate.
So, the first problem for you is that your "idea" might not even be patentable matter after Alice Corp. Patent practicioners have scrambled for more guidance from the USPTO (issued in Dec. 2014) and the Federal Courts. One comment actually likens the problem with the case to the problem with obviousness that existed before Congress (yes, they actually solved a problem) wrote Section 103 of the Patent Law.
The bottom line is that if the experts are still looking for help, the novice would be best not to swim in these waters.
As every lawyer on this page has said (and the above statements have outlined), this is not a simple answer and you should contact a registered patent attorney. The same holds true for your concern about "stepping on someone else's IP", a registered patent attorney will guide you down that path as well.
And, you should do so before you tell anyone about your idea. Just in case.

If you have developed new software from scratch, it is likely that there is something patentable there, from a novelty point of view, in the interface, menu order, logic flow, output format, something Big picture general concepts are rarely novel.
Whether the software is patentable from a statutory point of view (Alice v CLS Supreme Court decision) is another question. That case did not provide any bright line rules and has caused a lot of confusion and inconsistency in the lower courts. It will take a few years for the lower courts to give more guidance. The U.S. Patent and Trademark Office has provided guidelines with examples of inventions that can be patented and that cannot be patented. The guidelines are summarized on my blog at softwarepatents.com You want to be in a situation that is analagous to the DDR case, where you are solving a problem that did not exist before the Internet age. You will have trouble if you are just automating a process that was done by hand in the past.