What you are asking about is called freedom to operate. Freedom to operate is a challenging question to answer. Even the best legal opinion might not matter if you get before a jury of lay people. That said, what you need to focus on when evaluating a patent is what is described in the claims. It is pretty routine to find a patent where the specification seems to be describing broad areas of technology and find the claims are actually narrowly written. So focus on the claims first, especially the independent claims. Independent claims don't refer to other claims. To infringe on a claim, you need to implement each and every aspect of the claim. Thus, if a claims states something like: "...a phone sleeve implementing feature A, B and C" and your product only implements features A and C, you probably don't infringe on that claim. It doesn't mean there isn't another patent that covers just A and C however. When you find a relevant patent, look at the cited patents to get more possible patents to review. You can look at the file history in the US Public Pair site. This can be really useful to see what the examiner cited as prior art.
Doing your own research is important, but I can't emphasize too strongly that you should also consult with a patent attorney or agent. Doing your homework will make this interaction more efficient and thus cheaper. I'm not an attorney, but I've been told that if you have a legal opinion of freedom to operate, it could help keep you from having to pay punitive damages should you eventually lose an infringement suit. (Perhaps one of the actual attorneys on this site could confirm this information.)
There is an added element related to patent law regarding legal precedents. This may be particularly important in the current era, due to recent changes in the interpretation of eligibility requirements. Thus, you need to look not just at potentially prior art in relation to your invention, but also prior rulings.
Law review articles are a great place to do preliminary research, and the financial publications always publish stories on important patent cases. You can also generally find the rulings themselves online.