Texas was a republic. It joined the Union by treaty. There's a process in the treaty by which Texas could divide into five states. If we invoke that, and the last time it was voted on was 1985, the United States Senate would kick us out and nullify the treaty because they're not going to allow 10 new Texas senators into the Senate. That's how you secede.That's completely off-base, as the link makes clear, but I actually would welcome splitting Texas into at least two new states, on one condition: statehood for Washington, DC. It would solve the problem with the current bill to give the District voting representation in Congress, which is that it only applies to the House and not the Senate. Republicans, of course, would never agree to the admission of two new Democratic Senators, which is what Senate representation for the District would entail; but if it included the creation of an East Texas and a West Texas, both of which would plausibly be Republican strongholds, it could work out well.
Now, if Texans wanted to go for all five states, that could be problematic for the purposes of a balanced Senate. Assuming that all five states would send Republican Senators to Washington -- unlikely, given that there are, in fact, a lot of Democrats in Texas and that new states centered around, say, Austin or San Antonio would have a high proportion of Democrats -- we might have to consider creating new states out of our largest cities. New York City, after all, is practically its own state already.
But of course, this all assumes that talk of subdivision, much less secession, isn't just the product of irresponsible conservative rhetoric, which we really shouldn't encourage.