hope the following commands provide you with a good start.
Enable Error Codes
AT+CMEE – This command is responsible for enabling the unsolicited response codes (URC). When turned on, you will be able to better diagnosis problems that may arise from other commands issued. It is recommended that it be used so that you can quick discover the exact cause of an error result. Depending on modem manufacture, additional AT commands may be available that will enable another level of error reporting specific to the ME (any example would be AT+CEER).
* AT+CMEE=1 - Extended numeric codes
* AT+CMEE=2 - Extended syntax codes
AT+COPS – Variations of this command can be used to query your current network, to query the list of available networks and to set manual/automatic network selection. Examples:
* AT+COPS? – List the network you are currently registered on
* AT+COPS=? - List all available networks including the network that the SIM is currently registered on
* AT+COPS=1,2,”MCC MNC” – Attempts to manually set the network. If unsuccessful, leaves the modem in manual selection
* AT+COPS=0 - Puts modem into automatic network selection
Check GSM Registration Status
AT+CREG – This command checks GSM registration status. Without GSM registration, you should not attempt to attach to GPRS or performing any dialing function. By default, a modem will attempt to automatically register with a network without you having to invoke any action.
* 0,0 – SIM Error
* 0,2 – Searching
* 0,3 – Registration denied
* 0,5 – Connected roaming
* 0,1 - Connected
AT+CGATT – This command issues a GPRS attach or detach. This is not an automatic operation and will allow you to determine if the device is able to successfully attach to GPRS service. Once attached, this command will not accurately display loss of GPRS service. In some cases, it is possible to use other commands to bypass this action.
* AT+CGATT=1 - Attach
* OK – command successful
* Other CMEE code – See possible errors via CMEE result specific module documentation
* AT+CGATT=0 – Detach
AT+CGDCONT - Displays/edits/changes the configured APN. It is important that the correct APN be used or your SIM will not be allowed to connect to the Wireless Network.
* AT+CGDCONT? - Displays the current APN set (Example output, +CGDCONT: 1,"IP","apn1globalm2m.net","",0,0)
* AT+CGDCONT=1,"IP","apn1.globalm2m.net" - This will set the APN to what is specified. In this case, apn1.globalm2m.net.
AT+CGACT - The execution command is used to activate or deactivate the specified PDP context. It can be very useful in determining why you are unable to get a PDP session.
* AT+CGACT=1,1 where:
* OK – Command successful
* CMEE error code – See possible errors via CMEE result specific module documentation
AT+CIMI - Returns the IMSI
Check Signal Strength
AT+CSQ - Returns the Signal Quality
* +CSQ: <rssi>,<ber>
Alex, you should also check out this doc of common AT Commands across different modules, plus some good best practices. It was written by the certification manager at jasper.