Basically, the local prosecutors would work it out informally. If crimes were committed in different states, then each state would get their crack – if they wanted it.
For instance, take Timothy McVeigh. When he blew up the Murrah Building in Ohlahoma City, he killed something like 170 people. Most of these people were civillians (even though many were federal government employees). As such, the murder thereof was not a federal crime. A handful of federal agents were also killed, and that is a federal crime. McVeigh was tried in federal court for those murders (and other charges), for which he ultimately received the death penalty. The Oklahoma authorities could have prosecuted him for those 160-some other murders had they wanted to, but after he got the federal death penalty they figured it wasn’t worth the bother. Had McVeigh somehow gotten his federal conviction overturned, Oklahoma would have tried him separately.
Another example is the D.C.-area sniper case. Most of the sniper’s murders took place in Maryland or D.C. However, the first jurisdiction to try the suspects is Virginia. The snipers were actually caught in Maryland, but Maryland agreed them to let Virginia try them first because they’re both eligible for the death penalty there. Maryland doesn’t have the DP for minors. After the Virginia trial, Maryland, D.C., Washington, Louisiana, etc., might try them for murders committed in those jurisdictions. Or maybe those other states will not worry about it if the suspects are convicted, especially if they’re sentenced to death.