Edit the Access Control List (ACL)

Say your username is bubba. Have someone with Administrator privileges do the following:
Go to ​https://www.hosted-projects.com/ ,
Log in as the account holder,
Pull down Manage ACLs,
Hit Go,
and make an entry like:

[roms_sed:/branches/bubba_branch]
bubba = rw
csherwood = r
jcwarner = r
arango = r
rsignell = r

Check to Make Sure You Can See the Repository

Right-click and choose Repo-browser from TortoiseSVN.
Enter the URL https://svn1.hosted-projects.com/cmgsoft/roms_sed/
Now you should be able to look at the trunk and maybe some branches (depending on ACL), but bubba_branch won't be there yet.

Import a Copy of the Trunk

This process brings a copy of main code from the repository to your computer and places it under SVN control.
Make a directory...name it something meaningful to you, for example Bubba_ROMS_SED
Right-click on the directory folder icon, and choose SVN Checkout... URL of repository:
https://svn1.hosted-projects.com/cmgsoft/roms_sed/trunk
Checkout directory: Bubba_ROMS_SED
You should see a bunch of stuff stream by like:

Added: D:\crs\proj\Adriatic\bubba_roms_sed\ROMS  
Added: D:\crs\proj\Adriatic\bubba_roms_sed\ROMS\Tangent  
Added: D:\crs\proj\Adriatic\bubba_roms_sed\ROMS\Tangent\tl_rho_eos.F  
Added: D:\crs\proj\Adriatic\bubba_roms_sed\ROMS\Tangent\tl_uv3dmix.F  
Added: D:\crs\proj\Adriatic\bubba_roms_sed\ROMS\Tangent\tl_def_his.F  
Added: D:\crs\proj\Adriatic\bubba_roms_sed\ROMS\Tangent\tl_step2d.F  
...
Added: D:\crs\proj\Adriatic\bubba_roms_sed\Compilers\CYGWIN-g95.mk  
Added: D:\crs\proj\Adriatic\bubba_roms_sed\Compilers\OSF1-f90.mk  
Added: D:\crs\proj\Adriatic\bubba_roms_sed\Compilers\Darwin-ifort.mk  
Added: D:\crs\proj\Adriatic\bubba_roms_sed\Compilers\AIX-xlf.mk  
Added: D:\crs\proj\Adriatic\bubba_roms_sed\Compilers\SunOS-f95.mk  
Added: D:\crs\proj\Adriatic\bubba_roms_sed\makefile  
Completed: At revision: 243  

Click OK.

Create a Branch

In TortoiseSVN, choose Branch/tag. (To see this option in TortoiseSVN, you have to right-click on a directory that is under SVN control...but it does not have to be related to the project at hand).
From WC at URL:
https://svn1.hosted-projects.com/cmgsoft/roms_sed/trunk
to URL:
https://svn1.hosted-projects.com/cmgsoft/roms_sed/branches/bubba_branch
Click OK.
(stuff streams by...)

The branch will exist in the repository...you can repeat the steps above to make a copy of the branch on your computer.

Make Changes in Your Branch

You can make new files, change existing files, etc. Only existing files will automatically be under SVN control. To add new files, create them in a directory under SVN control (or copy them in from somewhere else).
Then you can right-click on the filename, and choose Add... under TortoiseSVN, or...
You will be given an opportunity later (see next step).
If you compile the code and generate a bunch of .f90 and .o files, or run the model and generate output, they will not be under SVN control unless you add them explicitly. That is usually what you want. (Storing output files here is probably a bad idea, because 1) they tend to be big and take a long time to tranfer to the repository 2) they are binary, so the tools used to compare them will not be useful, and 3) we don't have enough storage space at the repository.)

Commit Your Changes

Navigate to the top directory in your local copy of your branch, e.g., ../Bubba_ROMS_SED and right-click. Choose SVN Commit...
Commit to:
https://svn1.hosted-projects.com/cmgsoft/roms_sed/branches/bubba_branch
Message:
(add a meaningful comment here) Changes made:
(Will show files with changes. If the Show unversioned files box is checked, you will see any files you added to the directory. This is your opportunity place them under SVN control. Say you made one named foo that you want to add...check it and
Click OK.

Adding: Bubba_ROMS_SED\foo  
Sending content: Bubba_ROMS_SED\foo  
Completed: At revision: 244  

Work Cycle

You can Import this branch to another computer...that is the best way to synchronize, say, a desktop at work with a travelling laptop.
After that, the cycle is:
At the top local directory, right-click, and under TortoiseSVN Check for modifications. Click Check Repository.
Make changes.
Check for modifications or SVN Update (again..can't hurt).
Finally, SVN Commit...