What is a program similar to WinSCP?

Nautilus the default file browser has the feature of mounting remote files.

Go to File Menu > Connect to Server..

Other than that filezilla and gftp support sftp.

Since you are familiar with Winscp on Windows, I suggest that you try filezilla

FileZilla Client is a fast and reliable cross-platform FTP, FTPS and SFTP client with lots of useful features and an intuitive graphical user interface.

You can also install with the command line. Open terminal Ctrl+Alt+T and run following command:

sudo apt-get install filezilla

Or search on Filezilla in Ubuntu Software Center.

When you add a host, be sure to change from FTP to SFTP, and change the port number to ssh port 22 (or other custom ssh port if different)

Make the account type interactive.

Enjoy.

You could also use sshfs or rsync.

sshfs mounts your remote directory locally over ssh very similar to WinSCP and Nautilus.

The potential advantage of sshfs is that you can map users

sshfs -o idmap=server_user user@server:/directory ~/remote_directory

To automate the process, add an entry in fstab

sshfs#user@server:/directory /home/your_local_user/directory fuse idmap=user 0 0

See Ubuntu Wiki SSHFS

rsync will also sync files / directories and will work over ssh and has a graphical front end, grsync

See Ubuntu wiki rsync

Last you can edit remote files with vim (if you are interested)

vim scp://user@server//path_to/file_to_edit