Senate Districts elect delegates & alternates to the Central Committee. As a rule when a delegate drops out one of the alternates gets moved up to delegate and a vacancy is declared for the alternate position.
If a vacancy does occur, it's supposed to be announced at one meeting but the election for the spot is not supposed to be held until the next Senate District meeting. (I believe that is a state rule, not just the rule in my senate district). Depending on your senate district, these spots are more apt to be contested than other openings (like precinct chair). It helps if people on the senate district committee know you but it's not impossible to get elected even when they don't if you make a good case for yourself.
Check the DFL state site http://www.dfl.org for info on your senate district or see if it has its own website or Facebook page. Contact the chair and just tell him or her know that you'd like to get more involved and ask when they have their meetings. Attend a few of those. If you are not a member you may or may not be allowed to participate. Technically you shouldn't be allowed to vote, but you may be allowed to weigh in on issues.
(And sorry if you know most or all of this)