I have a samba share that I've created on another Linux server. On the server I've set the owner and group with chown to root:root for all files.

On my laptop I'm operating under user myuser with uid 1000 and gid 1000. I successfully mount the samba share with the following:

Now when I do 'ls -l /some/mountpoint' I see the files all listed with root for both owner and group. And when I try to do a simple 'touch /some/mountpoint/test', I get a 'Permission denied' error. But when I do 'sudo touch /some/mountpoint/test' it works. How can I make this work with my own 'myuser' account with uid 1000 and gid 1000 without having to take on root privileges (with sudo, su, or anything else)? I thought by entering the server's root credentials in the mount command it would be sufficient, but it seems not.

It seems like 'root' on the server and 'root' on the laptop are being treated the same here, which is confusing to me because I figured they would be different accounts because they're on different machines. If I change the file ownership on the server to a user whose uid doesn't exist on my laptop, doing 'ls -la' on the mounted samba share shows the ownership of that file to be a uid not a name, for example '501' or '502'. What happens in such a case where you mount a samba share with user ids that don't exist on the mounting system, I don't know much about this stuff but I would have assumed it would complain or not let you mount it!

You are right, those two are different accounts. But remember that root always gets UID 0 no matter which system you work on, your client will always show root as owner.
Samba will only tell the client the UID and GID of a file on the share. The client will then look in his own /etc/passwd if it can map those values to a user name, if it can not it will just show the UID/GID it got from samba.

The mounting is done through the user/password you supply in the mount command. As long as they are valid the mount should succeed.

You could also take a look at man mount.cifs for more information on the options for mounting.

I also would advice to use a credentials file for the user and password.

For example, this is my fstab entry to mount my music colection.
A good place to learn more about samba is samba.org, especially the using samba documentation.