You should seek out an attorney in your jurisdiction to determine if there are any state specific issues associated with this deed transfer in your state. In some states anytime a piece of real property is transferred the house can be reassessed for property tax purposes or there may be other state specific rules that you need to fulfill.
However, in general, you would draft a new deed from you to you and your spouse in the manner in which you want to hold title, and that may be a quitclaim deed in your state or an interspousal transfer deed or something of the sort depending on what it is called in your jurisdiction. You will have to do research or determine how title can be held in your state (or preferrably seek out an attorney to prepare a deed for you). There are legal consequences to holding title in certain ways that a real estate attorney will be able to advise you on. As a married couple, it is probably your desire that the home transfer automatically to the survivor if one of you passes away, and it is important to set up title in such a way so as to accomplish this.
It is generally easy to add a spouse to a deed by executing a quitclaim deed (or an interspousal transfer deed, if your state has one) and filing it with the county recorder. If both you and your spouse are US citizens (not merely US residents), there should not be any adverse gift tax consequences to doing so. However, you need to understand that if you and your spouse later decide to divorce, s/he will have an ownership interest in the property that you cannot easily reverse.
The information you obtain at this site is not, nor is it intended to be, legal advice. You should consult an attorney for individual advice regarding your own situation.
You don't mention whether you have a mortgage on the property, or other liens or judgments. If and when you sign a document adding your spouse, the pre-existing liens and judgments must be dealt with or they will remain as a prior lien on the property.
You don't shed secured debt by adding your spouse. That is the very nature of a "quitclaim" deed.