I purchased a key fob from a Ford Dealer whose parts department sells parts on eBay. Its best to go with an OEM key over some cheap aftermarket. Some dealers market parts on eBay to augment their usual sales to other dealers and local shops. I found this one on eBay, Galpin Honda is the seller and they are a Honda dealer in Southern California.
https://www.ebay.com/itm/151411713357?fits=Year%3A2010%7CModel%3ACR-V%7CMake%3AHonda&itmmeta=01HPRZ6Z8PQ6ZTBHQJT206GEKB&hash=item2340d7654d:g:Y~gAAMXQWlFRqRG6&itmprp=enc%3AAQAIAAAA0E5Gmcz5YUlEah4gfhM%2Bgxehs2auckuOLgvv8nS4a5%2FQR8ZNPlRsO%2B3j9T41WlILDMd41MIlv1pbh9ytOSq5GjkvjftfQ7QRCJck%2FEVJSMT7Aalp3es2Q4N0wuRbd8owX87W81ToaW0TCdleJ6e5nL0i2uaefe6WRUV3bnOLvVEJ7lek8P%2FNtc8Jwz0v8nLasIbD9Ad%2Fh9mDsSsZvAr34JQ7P7y99KccUodQ7yHcijGABTQjDU4%2FstggLhvFq3A3amZHpjjFLU8I5nkgmj3pKHA%3D%7Ctkp%3ABk9SR7b0m5-2Yw
I then took my new key fob to a local hardware store to get it cut. This is the riskiest part, as you need to find a place that cuts keys frequently and won't mess up your new key.
Once the key is cut, try it out on one of the CRV's locks not tied to the ignition (read: vehicle's onboard computers). The trunk/hatchback, glovebox, or locking center console are good candidates. Once you're sure the newly cut key works in the locks, proceed with programming. Drive home and do the programming there, in case things go awry so you're not stranded somewhere.
Once your new key is programmed and will start the CRV, drive the vehicle with the new key, but keep the old one with you anytime you drive just in case the new one fails (that can happen even with keys bought directly from the dealer). Once you're confident the new key works (a good threshold is a week's worth of vehicle use), pull the battery from the old key and put it away somewhere you can find it such as with the car's title.
Do not dispose of the old key! The keys that came originally with the car are hard coded into the Body Control Module (one of several computers that run vehicle systems). Losing or throwing away that original key means you would be compelled to take the car to a Honda dealer if you ever need to program additional keys in the future.
Good luck.