Here are some basic steps in purchasing a Manhattan apartment for the first time.
1- Decide on a Manhattan neighborhood
2- Get a pre approval
3- Co-op or condo?
3- Find a buyer broker
Also I would add to choose your real estate attorney well. Usually your buyer broker can help you with that. A real estate attorney usually chages around $2500 or so but some that do excellent work can be found for as little as $1700 depending on the price range of the property.
Additionally, beyond getting the pre approval make sure that the bank will finance in the building that you choose. Some buildings have sponsors that still own more than 10% of the shares(co-ops) or the apartments(condos) or a higher than usual percentage of tenants. This can complicate financing and is an area very often overlooked by many real estate brokers. This as a buyer can cost you time and money and add stress. So vet the building with your lender to avoid all of that! What are your tips for a first time buyer?