You don't provide a private key. You provide your public key. Your private key is used to prove control over your web-server.
You send the the public key in the generate CSR step:
Enter CSR
After generating your server's Certificate Signing Request as described in
Generate CSR, paste the CSR in the form below. Please make sure that it contains the complete header and footer "BEGIN" and "END" lines exactly as in the example below.
SAMPLE ONLY
-----BEGIN NEW CERTIFICATE REQUEST-----
MIIDCjCCAnMCAQAwdTEZMBcGA1UEAxMQaG9zdC5kb21haW4ubmFtZTEVM
BMGA1UECxMMT3JnYW5pemF0aW9uMRUwEwYDVQQKEwxPcmdhbml6YXRpb2
4xDTALBgNVBAcTBENpdHkxDjAMBgNVBAgTBVN0YXRlMQswCQYDVQQGEwJ
VUzCBnzANBgkqhkiG9w0BAQEFAAOBjQAwgYkCgYEAyZ1dYomQ4jhSr6f
G3GYxjS4B837+y3A6xIM9OVXV4ZnSIe9nOLHgdksQJpwaQeOZwWeqifte
hrJ/s55PvPxok+Tqq0t7BfMkkUSuiYnFdUo1OpDPdw3cEaP9WWSrduouI
Vnq2AWTDw2ykyxKg6neb2vYTZRvbot7M578Vvh6P8CAwEAAaCCAVMwGgY
KKwYBBAGCNw0CAzEMFgo1LjAuMjE5NS4yMDUGCisGAQQBgjcCAQ4xJzAl
MA4GA1UdDwEB/wQEAwIE8DATBgNVHSUEDDAKBggrBgEFBQcDATCB/QYKK
wYBBAGCNw0CAjGB7jCB6wIBAR5aAE0AaQBjAHIAbwBzAG8AZgB0ACAAUg
BTAEEAIABTAEMAaABhAG4AbgBlAGwAIABDAHIAeQBwAHQAbwBnAHIAYQB
wAGgAaQBjACAAUAByAG8AdgBpAGQAZQByA4GJACB3C0g9psK0+V+N/Me1
JsG39vonCPQBdOwNp6zHJSPCU3FwQ0SgFpEQNy6HEn79I0CMrU93q9Hh1
TQtd2YU6lWHQunXrIcytmAFVjhibNX6Dp1e41Wjc2N4ilJyy1GFss686c
dZt2GP6y04I74/OvkW2Wf9nezUrMrESM2PP4B1AAAAAAAAAAAwDQYJKoZ
IhvcNAQEFBQADgYEAg4+QHTvkP5CG+WcGnrhKiMkJnMP6QEsds40obUDS
dGtEupQz8C+4xoMd1aM68q9Ri6Va+JTeuhKHxLz9hT/KUJhNBy0sRfnx+
JkQdrKG69UanTwvLqXINh9xChw9ErIto/2kZI5kl2KYQdiOqTv6p0GEUP
Rq/MD52Zy3bOzSRF0=
-----END NEW CERTIFICATE REQUEST-----
Edit: I went through the steps of generating a more expensive wild-card cert.