You typically have a 60-day window to enroll in COBRA or a Marketplace plan. If you miss this window you'll have to wait until open-enrollment begins for the next plan, you have another qualifying life event or coverage begins at a new position.

COBRA is usually very expensive however since your employer no longer helps with the premium payments. The Marketplace is good for people who qualify for assistance due to their income or have major pre-existing conditions.
There are also private market plans that have year-round enrollment but the preferred rate options are based on good health. They're good for people who are relatively healthy and make too much money to qualify for a subsidy.
If you have any Dental work that needs to be done, do it before you lose the coverage. Dental insurance has a limit on how much they'll pay out, typically $1,000 or $1,500. If you get Dental insurance that isn't through an employer they all have waiting periods on them for basic or major care (6 and 12 months).

Let me know if you have any questions I can answer for you.