One way to accomplish this is to have a court appoint a special master to sign the deed. You would need to file suit and then get an order from the court appointing an individual (such as a lawyer) to sign the quitclaim deed in lieu of your husband.
I presume your question has to deal with the procedural aspects of filing a QCD. The QCD will need to be in the proper format for eventual recording. The QCD will need to recite the proper language to convey the Grantor's interest in the subject property to the Grantee. The Grantor will need to sign the QCD and have his/signature notarized. There may be an excise tax due and owing unless a recognized exemption applies. A Real Estate Excise Tax Affidavit will need to be completed showing the tax due and owing or the Washington Administrative Code (WAC) exemption. Once the documents are prepared, they are then taken to the county courthouse for eventual recording. There will be a fee for recording the QCD. If your ex-husband is unwilling to sign a QCD, you should consult with counsel about a possible quiet title action. Make sure to have counsel review the underlying loan documents (if any) to make sure there are no unforeseen issues (ie: due on sale) involved.
This answer is merely for general informational purposes only and does not constitute an attorney/ client relationship. You are strongly advised to consult with an attorney licensed in your home jurisdiction to get detailed advice on your legal matter based on the laws of your home jurisdiction and case facts.
You should review the specific facts with your attorney to find out your legal options.
You should review the decree of dissolution of marriage to see what the court ordered you and the former husband to do. It may be that the court awarded the husband a share of the house. It may be that the husband has a certain amount of time to sign the necessary documents to transfer the house to you. Without seeing the decree, no one can tell you what the court ordered.
"What do you need to do to file a quit claim deed in the state of Washington?" The factual answer would be include: preparing a document with the statutory elements of a quitclaim deed (including notarization of the grantor's signature); the document must meet the formatting requirements of the recorder's office; preparing a real estate tax affidavit form; presenting the documents to the recorder's office; and pay the necessary fees.
You likely are asking not just what is involved with the actual deed but how to get your former husband to cooperate. You likely will need the help of an attorney to achieve your goals.