Time to open the terminal and see what's going on:
My username is jmxp, so whenever you see that, substitute your own username.
Open Terminal and navigate to the folder you're working in. Then look at the file permissions:
cd Documents
ls -cla myfile.txt
-rw-r--r--@ 1 jmxp staff 2444 Dec 14 12:55 myfile.txt
There are two keys to this output. One is the owner of the file. You see in this output jmxp and staff. jmxp is the owner, and staff is the group. The important thing is that I OWN the file.
The second important piece is the permissions of the file:
-rw-r--r--
AFTER the first dash, you'll see rw- r-- r-- These are the three flags of permissions for three different ownership options.
rw- = Users
r-- = Group
r-- = Other
In this case:
- The owner jmxp has rw (read write permissions)
- The group staff has r (read permissions)
- OTHER has r (read permissions)
Look at the file you're trying to manipulate and ensure two things:
1) You OWN the file
2) You have at least rw permissions
Feel free to paste your results back here and we'll go from there if your permissions are hosed.
PS You probably need to check the permissions of the parent folder as well:
cd /Users/
ls -clad jmxp
drwxr-xr-x 27 jmxp staff 918 Dec 14 03:00 jmxp
The "d" means this is a directory. The owner is jmxp (good), the owner has rwx permissions which means read, write and execute. The group has r-x which means read and execute, other has r-x which means read and execute. Come to think of it, I'm going to go fix that

Nobody else needs read in my home.
After fixing the permissions to remove group and other read/execute permission, here's what my home looks like now:
drwx------ 27 jmxp staff 918 Dec 14 14:35 jmxp
Notice the change from drwxr-xr-x to drwx------
This means group has no permission and other has no permission, only the owner can read/write/execute files within /Users/jmxp