All Indian citizens need to apply for a visa in the following ways:  (Ref: Visitdubai.com)
Airlines such as Emirates, FlyDubai, Etihad Airways, and Air Arabia
Hotel or travel partners with whom you have booked a trip.  They can apply for a Service Visa (14 days), Tourist Visa (30 days), or Visit Visa (up to 90 days).
Other organizations based in the UAE
UAE residents (friends or relatives) can apply on your behalf subject to guidelines.