First, check the legal implications of trapping nuisance wildlife. In almost all jurisdictions there are either minimal, or exemptions to, regulations for property owners suffering damage regarding the trapping of wildlife. Be sure though to inquire as to what constitutes damage in your jurisdiction. In some areas it may be the mere presence of (as it is in GA and AL) or there must be a monetary loss (as in NC) or in some areas the animal must be in flagrante delicto aka caught in the act.
Also look into required permits and licenses. Some require none for property owners (as it is in AL), others require licensing for the capture of ANY wildlife (as it is here in GA) and others also require a seperate depredation permit (as it is in NC). Some of these licenses incur a fee and others do not. Here in GA homeowners and property owners can recieve a FREE 30 day trapping license upon request.
Once trapped there are further restrictions placed upon transport and disposal of wildlife. In almost all areas transport of wildlife, ie., possession, is governed and does require licensing and permitting if for no other reason than to make life easier upon conservation officers. Disposition is a whole nother can of worms as well. It can be broken down more or less into three groups; relocation allowed, relocation not allowed and the release on site or euthanize option. In the first group there are almost universal regulations upon geographic area of release plus almost always require written permission of the landowner where the release occurs plus a general prohibition upon release onto public lands. The second group usually bases their policy upon RVS (rabies vector species) protocols and require euthanasia of RVS (as it is here in GA) and possibly other species. Note, some stipulate or prohibit specific methods so be sure to look into that as well. The third group is a hybrid of the two former and gives one the option to either release the animal at the site of capture (such as in the case of removing an animal from a structure) or opting to euthanize if release on site would not solve the problem (as in the case of a coop raider).
Irregardless of specific regulations upon licensing, permitting, transport, relocation and euthanasia all jurisdictions have regulations as to the type of capture equipment available to be used and the methods of employment. For instance FL, CA, CO, NJ, MA all prohibit the use of foothold traps (in NJ the mere possession of is a felony). Almost all others have restrictions upon jaw size and placement (TN must use rubber jawed unless enclosed in a burrow or hole, GA 5.75" INSIDE jaw spread, AL 6" OUTSIDE jaw spread, MS no restriction on jaw spread). Snares are another area of contention. In some states all are prohibited yet in other there are a myriad of restriction such as loop size, height above ground, deer stop and closed loop size, BADs (break away devices), etc. Here in GA the use of snares is prohibited except for beaver yet the very same snare for beaver also is prone to the incidental catch of otter as well, all otter incidentally caught must be left at the site of capture go figure. Also the definition of a snare varies as in GA and AL the collarum device (probably the most safe, non lethal and humane canine capture device ever devised) is considered a snare since it uses a snare as part of it's design and is prohibited yet in AL powered foot snares (which are very similar in function to the collarum) are a legal device.
BTW, do not forget to learn the specific time intervals to monitor your traps in your trap check laws or the required labeling or tagging of your traps to provide owner identification of your traps.