I'll repost the algorithm that I've developed over the years for a-lines:
Assuming use of the Arrow kit with the long tube.
1. Positioning. Put a rolled-up OR towel or a-line armboard under the wrist to extend it. I like wrapping tape around the pt's thumb and using that to extend the thumb (by running the tape strip under the OR table armboard or whatever the arm is on)
2. Prep
3. Palpate artery. It's often more medial than you think. Also, it's easier if you insert your line a bit more proximally than some people are tempted to. At (or just proximal to) the wrist crease, the artery is SO shallow that it's hard to get into. Easier where it's a little deeper.
4. Nick the skin with an 18g or other large needle. Keep the needle really flat and use it like a little scalpel; you don't want to get into the artery! I think the skin nick helps hugely with letting the catheter slide in without getting hung up.
5. Enter the artery at about a 30° angle. When you see a flash, lower the angle about as flat as it goes against the pt's thenar eminence.
6. If the blood is still crawling up the tube at the low angle, advance the wire. It should go in like butter. If you encounter any resistance, withdraw the wire and go to step 9.
7. If the blood flow stops when you lower the angle, raise the angle back up and adjust the position of the tip of your needle a little so that you get good blood flow when you flatten the angle. If you get good flow, advance the wire. If you can never manage to get good flow with the flat angle, go to step 9.
8. Twist the catheter to advance it into the artery. If you've made a skin nick and the wire went in with zero resistance, I've found that the catheter very nearly always slides in without a hitch.
9. If the initial wire pass met resistance, or you were never able to get good flow at the shallow angle, raise the angle back up and plunge that thing through-and-through. Remove the needle, grab a wad of 4x4s to catch the mess, slowly back out the catheter and use a separate wire once you get good pulsatile flow. If you get piddly continuous oozing flow, you can try the wire but it's pretty unlikely to be successful.
10. Practice, practice, practice, practice. The way to get good at anything is just to do it over and over and over. You'll develop a feel for it.
This method sounds complicated but really it's not. And I've found it to have a really high success rate.