I've hunted with a rifle for several years,but I am thinking about taking up bowhunting. I guess my first question is the most important: How do I get started when I know absolutely nothing about bowhunting.

I'm in the same boat. Tell you what I learned.

Step 1- research..lots of it. Even in this forum...go back and search the archives.

Step 2- ask questions

Step 3 - find a good archery pro shop. A place that specializes in archery. Go down, ask questions, try different bows.

Also...know your budget you are looking at. It can get pretty expensive quick if you don't have things mapped out.

For instance...I skipped step 3 and bought a right handed bow. Although I'm right handed, I shot longguns left handed. Me being stupid, I didn't think about it. I can't shoot a right handed bow, my left eye dominance is too strong. So then I had to buy a lefty. Now i have a brand new right handed bow and can't shoot it. Maybe my kid will one day grow into it?
Also, the pro shop will help you pick the right weight, lentgh of arrows and such. So your not buying a 350 when you should be buying a 400.

Ask questions first, it will save you time and money

bowhunting.com has good info and videos. That's where I started. Not the biggest fan of some of the people but it's still informative. I'm still saving for my first bow but I prefer learning a lot about what Im getting into before I get into it.

Find a friend to mentor, guide and coach you.

Visit a well established archery shop. They will let you shoot different bows to figure out what fits best for you.

Don't go with the cheapest line. Save up your money instead for a mid point price or higher. You wanna cry once on your purchase.

This^^^

If you can find a friend, or coworker, relative, someone's friend of a friend.
You have to know somebody, and they are usually always looking for someone to go and shoot with.
Most of the time they will be more than glad to help and show what they know.
It usually doesn't take long to show you the basics, so even if you have to take notes, do it.
Also try to find an archery shop and go there during off hours where they aren't busy and you will get enough instruction to get you going.
Also read all you can to learn about arrows, and spine vs. bow weight and draw length, anchor points, release aids or tabs etc.
All important to know to have a correct set up for accuracy.

Honestly this is paramount.

Join a club or attend 3D shoots near you. Network with them and watch and learn. You can also look into Lone Star Bow hunters Association and see when they have a shoot or contact about shoots.

I would say go find a good archery dealer and develop a relationship. You can check prices in a few areas but if your "dealer' you choose is price competitive with what you have shopped around just stick with them, even if there slightly higher. You can get all your stuff from them and shoot there also. Most will have shooting lessons also you can buy. I would say although you could try to find a friend like mentioned above chances are that friend will not be as knowledgeable as a well staffed pro shop. Archery is historically a lonely sport....chances are your not going to find someone who you really can trust. So go to the shops. Keep it simple. I started with a compound in high school, went to selfbows, then traditional longbows and now back to compound. A common trait among all was keep it simple. If you build that relationship with a dealer then they will be a source to depend on when you have problems or questions. You can learn a lot with your own research also. Once your setup and shooting ok, go join a club. You can shoot their 3-d course and club shoots . With quality practice with a the right setup you will hitting fist size targets from your hunting range with consistency. And you will be ahead of about 75% of archers out there.

Besides a good pro shop, YouTube has a ton of great instructional videos

Whatever bow weight you can pull practicing, hunt with at least 5lbs under that . For a first bow get an adjustable @45lbs to 65 lbs. Start at 45lbs . Once you can shoot 5 good arrows 20 yards sitting on a stool, move up 5lbs and start over. You don't need to have a 70lb bow to kill any animal in texas. Start low and work up. You have to build muscles you have never used.

Go hang out at the pro shops. Remember fit the bow to you, not you to the bow. I would start out by finding out your draw length. Once you start killing them with a bow you will put the rifle in the closet. At least I did. Good luck