Place coffins where-ever you like. Early on during your fortress' life you probably won't have a public tomb or private burial chambers set up and waiting, and with the corpse there now you don't have time to build anything like that. Just find a nice out-of-the-way corner to put a coffin, have it built like any other furniture, and then set its options to allow it for use in burials and disallow pets. Your dwarves should place the corpse in the coffin pretty quickly.
Once you've dealt with one corpse, you'll start thinking about future corpses. Devise a burial plan for your fortress to deal with unexpected deaths swiftly, before they rot and cause distress to your fallen dwarf's friends. If you like you fortress to appreciate the dead, carve niches out of the main hallways and put empty coffins there. If you like them out of the way, dig out some catacombs on an unused layer somewhere and fill it with coffins. (Eventually a noble will request a fine tomb anyway—best to set aside some room for that sooner rather than later.) Maybe you want to place coffins around your statue garden so dwarves will visit the dead often.
Ultimately, the design of your burial plan is a matter of convenience, personal æsthetics, utility, and safety—just like any other part of your fortress.