Freezers are your friend in many cases. If you have paper items that are either actively molding or damp, get them into chest freezers to give you more time to implement suggestions from the resources in Susan’s post. Some other items like textiles can often also be frozen to give you more time.
Be mindful of what things are made out of if you choose to utilize this; leather could crack frozen when wet as could items that aren’t flexible enough to handle the expansion of freezing water. For these items, it’s most important to get them into a stable environment at cooler temperatures that inhibit mold growth while they dry out. Running dehumidifiers and air circulation from fans can be a huge help for creating these conditions without a lot of expense.