- Hip Waders
Paper and Pen
Water Pump or Wet Vac
Industrial garbage bags
Take photographs of the basement in its flooded state, and write down exactly what was damaged and to what degree. You'll need this for insurance claims and tax purposes, so gather it now.
This may take several days, as you do not want to saturate the soil; saturated soil means there's more pressure against the basement walls than there is inside the basement, which can lead to cracks and other problems. You may want to consider hiring a professional service to take care of this for you.
If there's mud, it's likely highly toxic. Shovel it out of the basement and dispose of it according to your state's guidelines. Any items that were floating in the water are likely ruined or contaminated: put them in garbage bags and throw them out.
Any soaked drywall and insulation will need to be removed and replaced; it's likely ruined, and may allow mold to grow if left unchecked. If the carpet has been saturated by outside water sources, it is also likely ruined and should be disposed of. If on the other hand your basement has flooded due to a broken pipe, your rugs may be salvageable.
Have a professional evaluate your water heater and other appliances in the basement. If they cannot be salvaged, remove them.