I'm going to start by saying I'm not the most experienced designer and I'm sorry if this question seems really silly but I am trying to tidy up a logo and I can't seem to get things to do what I want them to.
As you can see my lines are looking very untidy and I have been playing around with the different tools but haven't managed to get anywhere.
As we zoom in it is clear what a mess this is. I've tried playing around with the anchor points but it just ends up looking worse. I have tried looking on YouTube but had no luck with anything helpful to my situation.
Could someone please assist me so I can (a) learn by it and (b) move on to the next stage?
UPDATE #1
Thank you very much for your nicely structured and detailed answers, I really do appreciate it. However I am still not getting the results I'm looking for. It has worked for you but when I join the two anchor points I get the following:
What I did was hold down shift while having the direct selection tool selected (white arrow) and then went to object, paths, join and then this happens to the lines i try and join.
I gather I am doing something wrong, but can't figure out what. I also tried aligning the x/y points so they are a perfect reflection of each other but it does the same.
UPDATE #2
I have since managed to join some of my lines and have tidied it all up a little but for some reason other lines don't want to join and i get this message.
Is this something to do with my layers? I don't understand it if I'm honest. What exactly is a text path?