How do I transfer songs from my iphone to new laptop?

My old laptop crashed and I lost everything on it. The only thing I really needed from it is my music which is still all on my phone. About half my songs are not from itunes so they aren't saved through itunes. How can I get my entire library of songs from my phone onto my computer without having to purchase a file transfer program?

File transfer program? All operating systems have file transfer built in.
It is called "copy". Files are selected and then the copy option is selected and then a destination folder is selected and then "paste" is selected. In your exact case, the files to be copied are accessed by plugging in your phone to a USB port on the laptop. Now browse to the phone files by going to file explorer / this pc ---it is in the left hand list in file explorer.-and then to the phone now shown as a storage device on the laptop because you attached it. Browse into the phone to the location of the music files. Click to select (hold shift don to select more than one( the ones to be transferred and then right click and select copy. Now, go to the file folder on the laptop where you want to place them (probably the music folder/new folder and right click to paste them.
Pictures, documents and all other files are moved around on a computer and computer attached devices by copy/paste or cut and paste. By the way, unless the hard drive crashed on your old laptop, all of the original files are still on it and okay.

There's no way without special software.
Apple wanted to stop people from sharing music with friends, so they made it so you can't transfer music back off of a device to computer. Sorry.

Try using a program like iFunbox.

It lets you copy files to and from your device without using iTunes.

Depends on why your laptop crashed? If the laptop crashed because of hard drive failure, then follow the others' guidance.

If the laptop crashed for other reasons, you can pull out the drive and put it into a new laptop or put it into a HDD dock and rip the data right off the drive… Unless it's from apple… If it's from Apple, you now know why people slam on Apple so much and why you should go with any other possible OS/Manufacturer.