Unfortunately the process is designed to be pretty obscure and full of traps for the unwary, in part so that only people with the backing of one or the other major party have a real shot.
Here is the official primer from the New Castle County Division of Elections, which is where you would register as a candidate for a senate seat from New Castle County. https://electionsncc.delaware.gov/candi ... info.shtml
If you want to run as a Democrat or as a Republican, you file a declaration with the Division, but you have to pay a filing fee that is set by the county committee of the party (and gets paid to the party). The party committees don't have to set the amount until late June, a couple weeks before the filing deadline in July. The last couple election cycles, both major parties have set the fee right near the statutory cap, which is 1% of the salary for the entire term of office. I would figure the filing fee for senate this year is going to be about $1800. (It was $1781 for both parties in 2016.) For a representative seat, about half that.
If you want to run on a minor party ticket, you have to get that party to nominate you at its convention. The deadline for that is in August.
If you want to run as an unaffiliated candidate, you have to collect signatures from voters in the district to get on the ballot. No filing fee, but a big organizational obstacle. Those signatures would need to be collected and filed by July.
You can also run as a declared write-in. For that, you have to file a form with the division by September. Your name won't appear on the ballot, but people can write you in and they will count the votes written in for you. (They don't bother tallying write-in votes for anyone who doesn't file the form; otherwise they'd have to report that Bryan Townsend got a couple thousand votes and Genghis Khan got one vote -- from me.)