My dryer has a 4 prong plug the outlet is 3 prong. Also there is only one breaker for 220v, that is for the oven. Will I need another breaker for the dryer? And should I change the dryer cord or the outlet?

Check installation manual. If dryer can be wired using 3 prong cord it should be specified in installation manual.

First, as HK points out, the installation instructions must be reviewed for the manufacturer's requirements...

What kind of wire or cable supplies the three prong receptacle? Is it Romex or grey SE three conductor service cable?
The electrical code says that if you "do have" an equipment grounding conductor you'll need to install a new four prong receptacle.
If you "do not have" an equipment grounding conductor in the existing wire or cable (which means if you have SE cable) then you will need to check that the grounded service conductor is not small than #10 awg copper or #8 awg aluminum, and that this cable originates at the service panel...
The code section is 2011 NEC Article 250.140

OK, let's do this more clearly.

Quote:

---

My dryer has a 4 prong plug the outlet is 3 prong.

---

Both are still acceptable. My worry is your next statement. Is the "3-prong" receptacle for the dryer a standard 120V receptacle?

Quote:

---

Also there is only one breaker for 220v, that is for the oven. Will I need another breaker for the dryer?

---

If the only two-pole breaker is listed for the oven then you will definitely need a different circuit for the dryer.

Quote:

---

And should I change the dryer cord or the outlet?

---

Typically for an electric dryer you change the cord to match the receptacle.