What are the steps I should take with the military after getting married?

As soon as you have that offial marriage license, find out where the nearest base is and have her make an appointment with personnel. Otherwise you won't get any motivations while she is away, you won't be her next of kin.
Also both of you check out the Red Cross Hero care app

Don't get advice on RallyPoint about normal administrative matters. See your unit PersO and the Unit Chaplain. Helping you, with this, is what they get paid to do.

Take your official state or county marriage certificate to the nearest military installation and get your new spouse entered into DEERS as a dependent. Assuming you're Active Duty, having a dependent may change your status with reference to living in the barracks, drawing BAH and separate rations. When Mrs Keeling checks in for Basic Training, she'll need to update her marital status with the Army (again the marriage certificate would be good to have). The Army will sort out whom receives BAH between the two of you. Mutual spouse assignments will be a challenge, but after Mrs Keeling completes Basic and AIT she may be able to be assigned near you or at the same installation.