Karlie here from the Shopify Guru Team! Great question! This all depends on who you are dropshipping from. There are quite a few apps in the Shopify App Store that would allow you to do things such as importing products, keeping track of orders, and shipment. Depending on your dropshipper, you may have some luck finding an integrated app in the Shopify App Store, here!
Another alternative would be to speak to your vendor or dropshipper to get some assistance on setting up third party fulfillment with Shopify. Third party fulfillment would allow you to integrate your vendor with your Shopify Admin and have your vendor fulfill and ship off orders for your customers. Take a look at our excellent help guide which I would highly suggest walking through if you're wanting to set up third party fulfillment with your vendor.
If you haven't chosen your dropshipping vendor yet, then be sure you read through our Ultimate Guide to Dropshipping to make sure you have all of your basis covered to start. You could also consider looking into using Oberlo. Oberlo is an app that works through the Shopify admin to allow you to not only import products from Oberlo inventory, but it would also provide an integration when fulfilling and sending out orders to your customers. You can check out Oberlo, here!
I hope this helps, but if you have any further questions - be sure to ask and I would be happy to help!