Detailed answer — step‑by‑step under Delaware law

1. Confirm whether probate is needed.

   Not every small estate needs full probate. If the estate’s assets are very small or consist only of certain bank accounts with payable‑on‑death designations, probate may not be necessary. If probate is needed (for example, there are bank accounts, real property, or other assets that require a court‑issued set of “letters” to collect or transfer), proceed with the steps below.

2. Identify the correct county Register of Wills.

   In Delaware, probate matters are handled through the Register of Wills in the county where the decedent lived (New Castle, Kent, or Sussex). Contact that office for local forms and filing rules: https://courts.delaware.gov/registers/.

3. Learn who has priority to be appointed.

   Delaware follows an order of preference for who the court will appoint as personal representative. Generally, a surviving spouse or other intestate heirs with higher priority are preferred. If no spouse or higher‑priority person exists, siblings are among those who may be appointed. If several people at the same priority level ask to be appointed, the court will consider agreements among them or appoint the person the court determines appropriate. The court’s powers and the intestacy rules are in Title 12 of the Delaware Code: https://delcode.delaware.gov/title12/.

4. Prepare the required documents.

   Typical documents include: a certified death certificate; a petition or application for issuance of letters of administration (the exact name varies by county); an affidavit of heirs or list of next of kin with addresses; proof of your identity; and an estimated inventory or schedule of estate property. The Register of Wills office will give you the required local forms and filing instructions: https://courts.delaware.gov/registers/.

5. File the petition and pay filing fees.

   File the petition with the Register of Wills in the decedent’s county. The office will set the matter for review. The Registry will check whether a will was filed; if no will exists, the Registry can issue letters of administration if you are entitled and no one objects.

6. Provide notice and address creditor procedures.

   The Register or statute may require that notice of administration be given to heirs and that a notice to creditors be published or mailed. Follow the office’s instructions so creditors’ claims are resolved within statutory timelines.

7. Bond requirements.

   The court may require you to post a fiduciary bond to protect estate creditors and heirs. The bond amount varies with estate value. In some situations, all heirs can consent in writing to waive the bond requirement — the Register can explain local practice.

8. Receive letters and administer the estate.

   Once the Register issues letters of administration (or another form of appointment), you will have authority to collect assets, pay valid debts and taxes, and distribute property according to Delaware’s intestacy rules. Keep clear records, file inventories if required, and follow the Register’s directions about final accounting or closing the estate.

9. Distribution under intestacy.

   If your sister died without a will, her property passes according to Delaware’s intestacy rules (found in Title 12). The exact shares depend on whether a spouse, children, parents, or other relatives survive. See the Delaware statutes for full rules: https://delcode.delaware.gov/title12/.

Timing: The initial appointment often takes a few weeks after filing if heirs agree and paperwork is complete. If there are disputes or complex assets, appointment and administration can take much longer.

Helpful hints — practical tips for getting appointed and handling the estate

• Contact the appropriate county Register of Wills as your first step — they provide application forms and checklists: https://courts.delaware.gov/registers/.
• Gather key documents before filing: decedent’s death certificate, list of known assets and creditors, deed for real property, bank statements, and a family tree of next of kin.
• If multiple relatives want to serve, try to obtain written agreement naming a single administrator — that speeds up appointment and may avoid court disputes.
• Ask the Register whether a bond will be required and whether heirs can waive it in writing.
• Keep meticulous records of all estate transactions; you will likely need to account to heirs and may need records if creditors appear.
• If the estate includes out‑of‑state property (real estate, accounts), you may need ancillary probate in the other state.
• Consider consulting an attorney if heirs contest the appointment, if the estate is large or complicated, or if significant creditor/tax issues arise.
• Use the Delaware Code (Title 12) to read statutory rules on administration and intestate succession: https://delcode.delaware.gov/title12/.