"Go swimming" or "go swim"? How do you use "go" with another verb?

There are two options:

1.The typical structure is "go + gerund" (go + verb-ing: go walking, go shopping), which is normally used for outdoor activities. Examples: go bowling, go camping, go dancing, go diving, go driving, go hiking, go jogging, go skiing, go skating, go swimming, etc.

"Go" can change verb form (past: went riding, future: will go swimming, is going shopping).

2. It is possible to use "go ride" to mean "go and ride". For example: "I will go tell them." In this case "go" and "tell" are two separate actions, and we can also say: "I will go and tell them."
Other examples:
Let's go ride a bike!
We should go water the plants.
He wants to go see the film.

"Come" is used in a similar way:
Come sit with us! (Come and sit with us!)
Do you want to come have a drink at my place? (Do you want to come and have a drink?)