If flowers are in a vase you can empty the water, trim the stems and put the flowers back into the dry vase and place in a dry dark location, or you can hang the flowers in a dry dark place, (can take anywhere from 2 - 4 weeks to dry completely, each flower is different).
If you have individual petals or wish to remove the petals from the stem, lay flower petals individually on paper towel using tweezers to remove them from the stem and place in a dry dark location (can take anywhere from 1- 3 weeks to dry completely, each flower is different).
Looking for a quicker process? Google has many options to dry flowers in your oven or microwave.
Different types/styles of flowers dry differently. Roses take the longest as the middle core can be thick and take longer to dry completely. Daisy petals will sometimes drop off from the flower. If that be the case, let them finish drying as is, they can still be used.
If transporting individual flowers to a safe place to dry, DO NOT put them in a sealed container or bag! If you do, they will MOLD! Lightly wrap them in a paper towel or napkin.
If you are not sure the flower is dry to the core, like a rose, peal back the outer dry petals using tweezers. If the core is still damp/moist you can separate the petals with the tweezers or tooth pick to help dry it out completely.
Any flowers received with mold on them, inside or out are considered hazardous, unable to be used and will be discarded immediately.