Now, first things first. Texting is all about abbreviating, which is fine (you don't have to if you don't want to). But someone who cannot spell can come off as unintelligent or careless. So take the time to spell things or at least use a proper abbreviation so the person on the other end clearly understands what you are talking about.
Texting can be difficult as far as understanding exactly what someone is saying...text misinterpretations happen all the time! Remember that unless someone knows you well enough to know that you are really sarcastic, they might not get the sarcasm in your texts. Try to be clear, make your jokes obvious, et cetera.
Ok, now comes the actual flirting. Say you met someone but haven't been on a date with them yet. You could text and say "It was really nice to meet you...hope you're having a great day," or something like that. This should open up a dialogue between you and the other person.
Try not to text back at warp speed once you do hear back from the person. Texting back the next millisecond can come off as overzealous, clingy, and way too available. Try to wait awhile (at least 15 minutes, unless you or the other person is going to be away from their phone in a short amount of time), think about your responses, and don't try to carry on a conversation all day or evening. Part of text-flirting is being mysterious, not overly available, and playing coy.
Make sure to use smileys or wink faces to help convey what you are saying. Let them know how you feel without putting yourself too far out there. Write something like, "I had a great time last night. Let's continue that dart game soon." Something to let them know that you're interested, and would like to see them in the future. Don't go overboard and say things that you would never say in real life.
Lastly, keep it short. Many phones have a limit of 160 characters, and nobody likes reading paragraph after paragraph of text. If you have a lot to say, feel the person out as far as something like, "Can I call you tonight?" or "Too much to explain via text - I'll tell you more about it over drinks sometime." Be you, be courteous, let the person know you're interested but busy, and your text flirting should help take you further into getting to know this new person.