One simple thing you can do is have them sign a power-of-attorney("POA"). This document will give you (or some other trusted person) the power to act in your parent's place to manage his or her affairs. This can save a lot of time and anxiety if/when your parent becomes incapacitated.
My father-in-law is in decent health, but we have noticed that his memory is slipping considerably. He already has me take care of most of his finances (paying bills, filing taxes, etc.), but I do all of that online and there is no actual form giving me authority to do so.
He agreed to sign a durable power-of-attorney, which means that at any time my husband (the "agent") can step in and take care of any of his financial matters. This gives all of us peace of mind in case my father-in-law (the "principal") declines to a point where he is unable to perform the functions himself. It will save us a lot of time and paperwork trying to get the authority to take over his affairs.
There is also an ordinary POA, which becomes inoperative if the parent becomes incapacitated (I guess the reasoning here is that the parent would not be of sound mind if s/he wanted to revoke the POA). We opted for the durable POA because we want the document in place continuously and my father-in-law is unconcerned about giving his son access to all of his finances. In other words, he trusts us!
Note: all POAs terminate upon death, or by court order, and they can be revoked at any time (but if the person is incapacitated, that would be difficult to do).
The POA can be "general", as in our case, or "limited" if the powers are only to do one specific thing, such as sell a piece of property. There can be more than one agent, and the principal can decide if s/he wants the agents to act jointly (all must sign to make any moves) or severally (only one must sign). In families where there is a lack of trust---they do exist!---requiring that all sign jointly may alleviate some of the problems.
There is also a "springing" POA that only goes into effect upon a specific triggering event (for instance, the incapacitation of the parent).
There's lots to learn and think about, but if you have an aging parent and they are open to discussing their future financial affairs, a POA might be a good idea. A great article to get you started is here: http://www.agingcare.com/Articles/what-is-durable-power-of-attorney-140233.htm
Forms are available online and could be filled out without the help of an attorney, but each state has different guidelines so it might be a good idea to consult an attorney for assistance.