Certain ships, including your mothership and carriers, are able to construct and deploy drilling missiles (They used to be called mining missiles but I am pretty sure iirc they are called that now), which when launched travel towards an asteroid and explode, dealing damage to the asteroid. You are able to change their target while they are flying. When the asteroid's hp hits zero, they explode into a small cloud of harvestable debris. If you do not want to spend RUs on these missiles, you can use the force attack command to get your military ships to blow em up. Iirc to order a forced attack you do CTRL + SHIFT + click on the desired target (remember to have some ships selected for you to order or nothing will happen!)

Ah okay thank you.