If my neighbor passed away and left me her house but I want to “pass” it to my adult child, how do I do that?

There are a couple of different ways to accomplish what you would like...and you really should sit down and review each of them with a wills/probate attorney before you decide on which option is best for your situation.
If you want the house to pass to you adult child at a later date, then you can execute a will that provides for the gift.  Your will can also authorize your estate to pay any gift taxes that result.
If you want the house to pass right now, you can execute a couple of different types of deeds that either grant full or partial ownership.  For example, a lady bird deed would give you a lifetime interst in the house, but would cause the house to automatically pass to your adult child after your death.  This method tends to reduce the tax obligations for both households.  However, if you are in the middle of applying for certain government benefits, then it could be perceived that you are transferring the house with intent to defraud.  Because the method and the time for titling can be an issue, you really need to review your financial situation with a probate attorney to know exactly which type of deed conveyance will be most effective.