patenting a similar idea

Patents, for the most part, comprise improvements upon existing technology. In addition, you can patent different systems that effectively do similar things but do them differently. Search, for example, automobile transmissions or fuel injection systems or braking systems - there are hundreds of patents that do similar things but they may do them differently, and the trick is to claim your invention in a manner that is patentably distinct from known technology usually disclosed within prior patents. So, yes, you can possibly get your own patent if you draft your claims properly to clearly recite what your invention is and to patentably distinguish it from prior patents. You should consider your patent directed toward a system for accomplishing something or a method for accomplishing something.

It is difficult to answer this question on the vague terms of 'idea' and 'method' that you use. If I may use an example: the idea is to reduce global heating and a method would be reduction of CO2. If this would be your invention, but somenody else would have had the same goal but now by burning less fossil fuels, then your idea (if new and non-Obvious) would still be patentable over the idea that was already in the public.
Further if somebody got a patent on a method, you may not use that method. However, first you should be clear that it is a patented method and not just a patent application. Secondly, for a patented method the scope of the protection is given by the claims at the end of the patent. If you do exactly what has been mentioned in teh claims you would be infringing. If there are differences it may be that you are infringing, but there is a fair chance that you will not be infringing.
In your case it would be wise to contact a patent attorney to see where you stand.