The background:-

Android is a Linux-based operating system for mobile and hand-held devices, and like Linux, it bestows full power only to the 'root' user, that is, the power user or the administrator.  However,  Android phones for most part are 'locked', that is, users don't have 'root' privileges.  They can only use the functionality provided by the various applications and nothing more. This is done partly to ensure that users don't screw up the software on their phones and in many cases, to ensure that a user stays bound to a particular service provider. While the typical user would put his/her hands up if a feature or the lack of it frustrated him/her and leave it at that, I'd want to get my hands dirty and try and fix it.  This led me to the forums that discussed 'rooting', that is, means to 'unlock' the hidden powers of the devices, to be able to change things at will.  Rooting however comes at a price: the warranty is immediately voided and there is a very real risk of turning the device into a really expensive paperweight, in case things go wrong! 

A casual search of the terms 'Android' and 'Rooting' throws up a whole lot of data, but not all of it is easy to understand, or even relevant. While some articles describe ways to get super user privileges on the existing system, most talk about replacing the entire system with a different system.  I was more inclined to try the former than the latter, as I was pretty happy with the software provided by HTC.  I only wanted to iron out a few kinks, not have a completely new system which I may or may not like.
Sometime back, HTC announced that they were allowing users to 'officially' unlock the bootloaders on their phones and I grabbed the opportunity, as an unlocked bootloader is the first requirement to be able to obtain root privileges on a phone. The bootloader unlock process was pretty straight-forward,  and before long, I had accomplished it.  The next question was how to go about getting superuser privileges on it.  Once again,  there was a lot of information, but two webpages were particularly helpful:
http://androidforums.com/incredible-all-things-root/420788-how-regain-root-s-off-htc-unlocked-bootloader.html
and
http://www.addictivetips.com/mobile/root-and-install-clockworkmod-recovery-in-htc-salsa-guide/
It was not all smooth sailing, as the primary method, including the software listed and the method described didn't work for me. User scott85's comments on the first site were really helpful, and I successfully rooted my phone, that is, obtained super user privileges without changing the whole system. Let me sum up what it took, to successfully root the HTC Salsa, just in case anybody needs it.

DISCLAIMER:-
This is what I did to successfully root my HTC Salsa (Gingerbread 2.3.3) phone.
I offer no guarantees that these steps will work for you and and take no responsibility for any damage that may occur to your phone, if you decide to try these instructions out. The links provided and the packages referred are not owned/maintained by me and I'm not responsible for any content on those sites or in the actual packages.
ROOTING IS DANGEROUS AND MAY RENDER YOUR PHONE USELESS IF YOU GO WRONG. LET THE USER BEWARE!

How I rooted my HTC Salsa

1) Updated my phone's software version to approved Software number (1.12.720.5 for my region) by accepting the OTA update (HTC Twitter client).
2) Downloaded the RUU (only works on Windows) for my software number, from the HTC dev site, after logging in with a new account.
3) Installed RUU and completed the listed steps to unlock bootloader.
4) Formatted my sdcard in Fat32 format. 
5) Downloaded recovery image archive PH11IMG.ZIP and unzipped it to get 'recovery.img' which I copied onto my sdcard.
6) Downloaded superuser application files archive Superuser-3.0.7-efgh-signed.zip which I copied onto my sdcard.
7) Put my phone into HBOOT mode and THEN attached phone to computer with USB cable. 
8) Ensured that the phone was detected by the computer and then executed
fastboot flash recovery recovery.img
9) The fastboot command reported the successful flash.
10) Rebooted my phone into HBOOT mode, and then into recovery mode. This brings up the 'Clockwork Mod' recovery tool.
11) Chose the 'Install zip from SD card' option.
12) Chose the 'Choose zip from SD card' option.
13) Selected the Superuser-3.0.7-egfh-signed.zip file and selected the 'Yes, Install' Option.
14) Got a 'Success' message and rebooted to normal mode to find the 'superuser' app installed. The rest of my apps and original system were unaffected.

Some really cool apps that I found, for my newly rooted phone. All these apps are available for free, in the Android market. While not all of them require root, they make a lot of sense on a rooted phone.

1) Titanium Backup:  Very powerful utility to backup and manage applications.
2) BusyBox:  Enables many, many useful system commands.
3) Terminal Emulator: Allows you to use all those useful commands enabled by BusyBox.
4) SSHDroid: Allows you to setup an ssh server on your phone, allowing you to log in to your phone from another phone/machine on the same network (wifi)
5) ConnectBot: Allows you to log in to other machines/devices on the network (wifi).
6) RomManager: Check/fix file permissions, reboot into recovery and a lot of ROM related functions (I don't use most of them).
7) Link2SD: Allows you to combat the dreaded low internal storage space problem.  This deserves a whole post.  Coming up soon.
8) Root Browser: Allows you to browse all directories and cut/copy/paste/move/delete files/directories. I prefer the commandline, but this is a nice graphical tool.