AFAIK, this is the process (it MAY be different for you, Donks, since I can't find any info on filing in NE) I'm using, in it's place, the procedure for FL:
THE MOTION:
You'll go to the CoC and request a Notice of Motion and Order (a form, really). On it. you will HAVE to write down ALL the names of the parties from the ORIGINAL claim (which is WHY you need all the documents from your FIRST case). You'll also need their addies, too. And yours, of course.
You'll need to write down on the form the Conciliation Court case number, too. That, too, should be in the sheaf of docs from your first case file.
Write down the hearing date that you're hoping for (no guarantees that you'll get it, though. Depends on what else is on the Docket). Here in FL, the best days are Thursdays as that's the day of the week that they hear new motions on old trials (for lack of a better term) ... ask the CoC what day they reserve for hearing motions.
You'll need to state the REASON for the motion.
You'll then need to sign the motion in view of the CoC.
From there, it's the process serving! Depending on your state, you will either need to have someone serve the papers on ALL parties, or you could possibly get away with a public ad in the local newspaper ... or delivering the summons via CMRR. That will depend on your state. So ask the CoC. NE seems to be a friendly state for self-helpers, so they should be able to tell you (since it's procedure rather than interpretation). Proof of service usually needs to be returned within 3 days of the hearing date. But again, that depends on your state. NE seems to be VERY lenient in terms of service, so that may not be a hard and fast rule.
Then, once all of that is done, you have to show up for the hearing. If the opposing party declines to answer the summons or appear, you're home free!!