You will be able to test out various features of the upcoming sequel starting next month.
Destiny 2 will be released on September 6th on PlayStation 4 and Xbox One. The PC version will launch a bit later, in October. But if you are impatient, anyone who preordered the game will be able to try it out during the beta starting on August 18th (PS4) or August 19th (XO). Others will join on August 21st.
The beta will include the starting story mission titled Homecoming, a single co-op Strike mission, as well as part of the multiplayer mode. The PC beta is scheduled for a later time, so you should wait for the details.