How to put songs onto iphone 4 without deleting old ones?

When I synced songs from my iTunes to my iPhone 4 it worked, but when I added more, it deleted all the old ones I had and only kept the new ones I just added. I didn't sync any from anyone else's account. It saves the music on my computer and in my iTunes but it erases them off my phone when I add new ones so is there anyway I can add songs and keep the old ones I had without having to go re-sync them all?

It is impossible to do so, unless you have a copy of the old songs that were already on your iphone in your itunes library. Because itunes only syncs files that are in your library and replaces them with ones on your phone.

There was a trick to do so in the past, but I'm unsure if it still works. If you enable to the sidebar (View, on top, then sidebar), drag songs onto the device in the sidebar. If not, you'll have to use another program like I-FunBox. Or CopyTrans.

I never sync any of my Apple devices to put music on it. Instead my iTunes is set for manual management of music and video. I almost never have problems putting music on my iPod and obviously much fewer than those complained of in questions like yours which are posted here in the thousands - including loss of music to put songs on my iPod.

Manual management is just clearly superior in every way and it works on iPods, iPhones and iPads both new and old. I've tried it on first generation nanos, iPod 4, iPad 3 and iPhone 5

You enable manual management by bringing up sidebar in iTunes (ctrl S if you don't have it up already) and clicking on the iPod tab. The main window should show you the main summary for your iPod. The box for the manual management option is at the bottom of the page (it's probably already checked).

That's basically it. Now you can just drag the songs from whatever folder they're in in WIndows and drop onto the iPod tab on iTunes sidebar.

Every time you update iTunes, you need to reboot your computer.

ITunes deletes songs, because your iPhone has songs not in iTunes library.

If you want to keep adding new songs to iPhone using iTunes, it will still delete your songs.
So you need to:

1. Do not use iTunes anymore. There are a lot free iPhone transfer, like Syncios, which can transfer music and other stuff between iPhone and pc smoothly.

2. Use free iPhone transfer to transfer songs in your iPhone to iTunes library, always keep iTunes having the songs in your iPhone, then you can use iTunes to add new songs and not deleting old songs.

If you choose to use free iPhone transfer, this tutorial maybe helpful:
http://www.syncios.com/how-to-transfer-music-from-iphone-4s-to-computer.html