I just installed one within the last couple weeks and it is not hard at all. I normally don't do stuff like this but when I was told that it would cost a couple hundred dollar's for someone else to do it, I broke down and did it myself.
Drain the old tank.
Disconnet the earthquake strap.
There are three connections. Cold Water coming in, Hot water coming out, and a line connected to a pressure relief valve. The only thing that isn't completely straight forward about it for me and my tank was that the connections on the new one were in totally different places than the old one. On the old one, the three connections were on the side of the tank. On the new one they were on the top of the tank. So, none of the pipes/hoses fit. So, you just go to Home Depot (or whatever) and buy longer, braided hose to make the connections. Put white teflon tape on all the connections and you are good to go.
The tank isn't all that heavy.
In looking at your picture, the connections on your present tank are on top. The tank itself is in an outside closet. It looks to me like there is nothing to it. Actually, let me back stroke here for a second. It looks like yours is gas. Mine was electric. That changes things a little bit, but it still shouldn't be any big deal.
FWIW: I would replace it if it is more than six years old. Mine looked pristine. Worked fine. But, it was eight years old and like yours, it is in a closet like that. If it started leaking and I didn't realize it, it might leak into the house, might screw up the drywall, might start a mold problem.................... So, I figure a little preventitive maintainance before any of this happens is money well spent.
In my parent's house where I grew up back east the hot water tank is in the basement. When it would go bad and start to leak it was obvious, and it was leaking on a concrete floor that had floor drains. In the west, our tanks are in sheetrocked closets where some serious damage could occur if they were leaking for any length of time and we didn't realize it.