That's a difficult question to answer without knowing more. Being the only person with a radio usually isn't that helpful. You need to know who you can communicate with and what modes and frequencies they use. In the U.S., I'd suggest staring with trying to contact RACES (Radio Amateur Civil Emergency Service) or ARES (Amateur Radio Emergency Service) groups in your area. Typically one is stronger/more organized then the other. RACES groups are affiliated with a local emergency management agency, while ARES groups are organized by the ARRL (American Radio Relay League) and are connected with "served agencies". These might be Salvation Army (who also has their own group SATERN), the Red Cross, local hospitals, etc.
You may also want to explore connecting with CERT (Community Emergency Response Team). While RACES and ARES are more focused on supporting responding agencies, CERT is more about helping your neighbor, but frequently has a radio communication element to it. My stake has been holding CERT training. You'll probably want to explore a bit to find the right group that fits your interests.
Once you know who you will be talking to, you'll know what kind of equipment you'll need. Usually it will be a 2 meter or 2m/70cm transceiver. Either a hand-held or a mobile. There's also that little detail of getting a license. Which one you needs depends on if you need to use HF or not.
ARRL does have some good training, but local groups may have other requirements.