So there's going to be multiple intros for the different characters that end up traveling with the Doctor. Here is River's intro.
The doctor had just pulled a flying River Song in through the doors of the TARDIS
Doctor River?
River hello, Doctor! How are you? Or should I say, when are you? Well, come on, follow that ship! After quite a bit of running around the TARDIS core and arguing with each other about blue switches and stabilizers, they finally managed to land the TARDIS.
River Aaaaaand we've landed.
Doctor No we haven't. It didn't make that sound. River looked at him weird. Ya, know, that hweeeee-haaaa hweeeee-haaaaaaaa weezing sound that it does whenever it lands.
River It's not supposed to make that sound, you leave the brakes on.
Doctor I don't care. I like that sound. It's my sound.
River whatever. Let's go exploring!
Doctor uh, no! You don't know what's out there! You can't get hurt, I haven't met you yet.
River oh, stop treating me like I'm dainty. I'm not a rose.
Doctor oh, I wouldn't say your a rose. Roses are strong, but there is only one person I know that is a rose. That is the only person who will ever be a Rose to me. My Rose.
River oh, stop going on about the girl who left you for yourself. I, your not-yet-wife, don't feel like hearing you, my-used-to-be-but-also-not-yet-husband, babbling on about your babymomma.
Doctor my what?!
River oh, worry evident in River's Face you don't know yet.