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Do not soak or over-water the cutting or divided plant or it may rot and not take root. Water spray works well for many plants but take care with succulent and furry leaves. They are best only watered directly at the soil level, otherwise the combination of humidity and water may encourage fungal growth. If you can feel resistance, you'll know there are roots. Most plants will root within 6 - 8 weeks, although some species of plants can take up to 12 months! Do some research  on the plant if you are not sure. Most common garden variety plants will root quickly.
Keep the soil moist. Pull the cutting or divided plant gently in about 6 - 8 weeks. Transplant to a larger pot or the garden when the seedling is well-established.