Posting to php server using SIM900 GPRS with AT commands
After much googling and mashing together various answers, I got it working.

Here's the AT command sequence. You can test this from start to finish, you'll just need to confirm the APN of the carrier you're using.

// My comments are here
Command to send is here             Expected responses are here

// See if the SIM900 is ready
AT                                  OK

// SIM card inserted and unlocked?
AT+CPIN?                            +CPIN: READY
                                    OK

// Is the SIM card registered?
AT+CREG?                            +CREG: 0,1
                                    OK

// Is GPRS attached?
AT+CGATT?                           +CGATT: 1
                                    OK

// Check signal strength - should be 9 or higher
AT+CSQ                              +CSQ: 14,0
                                    OK

// Set connection type to GPRS
AT+SAPBR=3,1,"Contype","GPRS"       OK

// Set the APN - this will depend on your network/service provider
AT+SAPBR=3,1,"APN","wholesale"      OK

// Enable GPRS - this will take a moment or two
AT+SAPBR=1,1                        OK

// Check to see if connection is correct and get your IP address
// (I hid mine here, but you'll get a real IP back)
AT+SAPBR=2,1                        +SAPBR: 1,3,"0.0.0.0"
                                    OK

// Enable HTTP mode
AT+HTTPINIT                         OK

// Set HTTP profile identifier
AT+HTTPPARA="CID",1                 OK

// Put in the URL of the PHP webpage where you will post - 
// the URL below is a test server so you can use it in testing
AT+HTTPPARA="URL","http://posttestserver.com/post.php"
                                    OK

// Tell the SIM900 how much data you'll send (18 bytes here) 
// and how long to wait for a time-out (10,000 ms here)
AT+HTTPDATA=18,10000                DOWNLOAD

// Key in the data you want to send after you get the "DOWNLOAD" prompt.
vdc=12&amp;adc=3&amp;rel=8                  OK

// Post the data - wait a second for the response
AT+HTTPACTION=1                     OK
                                    +HTTPACTION:1,200,142

// Read the response - www.posttestserver.com will give you a 
// URL where you can confirm that it's working
AT+HTTPREAD                         +HTTPREAD:142

"Successfully dumped 0 post variables. View it at 
http://www.posttestserver.com/data/2016/04/28/14.19.041655610622
Post body was 18 chars long."
                                    OK

// Close the HTTP connection
AT+HTTPTERM                         OK

// Disconnect the GPRS
AT+SAPBR=0,1                        OK


Edit to add: Here are the sources I used to put all of this together, along with help from some folks I asked in my lab.  


https://vsblogs.wordpress.com/2013/11/28/tcp-connection-over-gprs-using-sim900-and-at-commands/  
http://www.raviyp.com/embedded/194-sim900-gprs-http-at-commands  
http://www.dsscircuits.com/forum/index.php?topic=82.0