Note: Please post questions in the Rubberside or PM me...

Savages have 12volt 14amp batteries...  Yuasa YB14L-B2

The stock battery is a wet cell. and water levels must be checked periodically.  At least twice a year.  
You can't check it on the bike,... you gotta' pull it out to see the levels on the side. (bummer!)  
Holding it to the light helps.
If low, use distilled water to fill.
A small turkey baster works well for filling the cells.  Each cell must be checked and filled individually. Each yellow cap covers the fill hole of one cell.

Fully charged, a good battery should read at about 12.6 volts with a multimeter.  Less than 12.1 volts means your battery is only working at about 25% of it's full power.  It either needs to be charged, or replaced.
If you take a reading immediately after charging, you may read up to 14.5 volts,... but that won't hold.  It'll drop down to a maximum of 12.6 after a short cool down period.

Always connect the negative terminal last, to prevent shorting when connecting the positive terminal.
Always disconnect the negative terminal first.

Charge dead batteries with a charger rated at 2 amps or less.
6 to 8 hours @ 2 amps
10 to 16 hours @ 1 amp
20 to 30 hours @ 1/2 amp

You can jump-start a dead motorcycle from another bike or a car.
If you jump from a car, do not do it with the car running!
.  The output of the car's charging system can damage the electrics of your bike.  It's no strain on a car battery to jump-start a bike without the engine running.

When the stock battery dies, (will no longer hold a charge), it can be replaced with a "gel cell"...  These batteries are sealed, and are therefore don't need to be checked (nice), and they will hold their charge longer than a wet cell.
Big Crank is very a popular replacement....
http://www.bigcrank.com/suzuki-l650-savage-all-battery/ETX-15L.html
also...
Batteries Plus has a good one if you have store near you...
http://www.batteriesplus.com/product/40578-X2--15L-X2Power%C2%AE-AGM-Battery/...

* If you get hard freezes where you live, it's best to have the battery or the whole bike stored inside.  If the water freezes it can crack the battery case.  So I've been told...

In recently searching for a replacement AGM battery I have noted that following the reference chain from YB14L-B2 to the glass mat AGM style often leads to reversed + / - terminal positions.    This is because there are folks out there that are assuming for you that you have enough lead length that it doesn't matter.    On a Savage, it matters.

Your required battery size is 5.31" x 3.5" x 6.56"  (134x89x166mm) and you want your + terminal on the right hand side.

I found the best prices and correct size and terminal placement this time around when looking at YTX14AHL-BS batteries -- take care to look at your dimensions and terminal placements because I found backwards terminal batteries even inside that search.

Interesting addition -- what was actually shipped to me was a generic UTX14AHL battery, but it was the right physical size and terminal placement.  

The UTX14AHL battery fit neatly and cranked the bike right on up, for $38 shipped to my door.   Brand was Adventure Power, made in China.  Seller was misc Ebay sellers.

I think the old style wet lead acid batteries are costing more and more each year ($65 is common now) and these new AGMs are used in all sorts of alarm systems and such, so they are relatively more commonly available and at an increasingly cheaper price.

Since these AGM batteries ship well I would not fear buying one from any vendor who obviously moves his stock fairly quickly.   Check the promised warranty period -- it will take you less than 30 days to spot a loser, so keep your packaging for at least that long.

Learn to read the date code stamped by law in the top of the battery -- mine was built year 13 week 48  (2013 week 48) so it isn't brand new.   I have potentially lost a full year of service use on this one.   People tend to forget this about AGM batteries, that you never can get them in a brand new just manufactured condition.

Since AGM batteries generally last 3-5 years from manufacture there is some advantage to buying an old style wet lead acid battery that you put the acid into it just before putting it into use.   This give you the full 3-5 years of use life since you "manufactured it" on the day you put the acid into it.

Plus, if you find a good good price on some dry cell w/acid set ups you can buy a couple and store one in a closet, knowing it will be fresh when you need it.

and...consider installing a trickle charge plug when you install the new battery.  that way if you go awhile without riding your battery will be fresh and charged to start the bike.  It should also prolong battery life.

Thanks for creating this thread! As a newb, I found this article very helpful, so I'm posting a link and excerpt here so that other newbs might potentially benefit:

https://www.throttlexbatteries.com/details.aspx?p=A4D3D61DCEB3C859&ppid=59924...

Excerpt:
"Gel Cell Batteries vs. Absorbed Glass Mat (AGM): What’s the Difference?

So your buddy is telling you to get a gel battery.  He says they last longer, can't spill acid all over your ride and have more cranking power when you need it.  His opinions can all be considered fact except for one; he doesn't know the difference between gel and AGM batteries.  Common mistake but now you can set him straight after this quick read.

In recent years, an alternative to conventional, flooded (spillable) lead-acid powersports starting batteries has been introduced: the valve regulated lead acid (VRLA) battery. These types of batteries offer many advantages over conventional flooded lead-acid batteries, including:

-   can be mounted and used in almost any position (versus conventional batteries, which must remain upright)
-   are sealed and non-spillable
-   maintenance-free
-   no fume emissions
-   more resistant to vibration

There are, however, two distinctly different types of VRLA batteries: gel batteries and absorbed glass mat (AGM) batteries. AGM batteries are often mistaken for gel batteries, due to their similarities, but if you're looking to understand more about how your powersports battery works and how to find the best battery for your particular ride, it's important to understand the key similarities and differences between gel and AGM batteries."

Thanks, JLC. That's helpful for a newb like me. I would also add that I connected my battery to a charger for the first time today, and I read in the instructions that the charger works with floodable and AGM, but NOT Gel-type (I have a "Centech 12 Volt Deluxe Battery Maintainer and Float Charger"). So good reminder - READ THE MANUAL

There is also mention on the forum about the differences between chargers and tenders, and charging dead batteries, as Serowbot mentioned above (versus partially charged ones?). Again, there appears to be some charging-unit-specific details here, because my charger says not to use it on completely dead batteries Again, that MANUAL really helps!

Just for those who have not yet had the joy of accessing the battery on the Savage/S40, approach it with a heapin' helpin' of patience and perseverance. It's not a 5 minute job! See my post on Rubber Side Down. Once you do, adding a pigtail for a plug-in trickle charger is simple, easy, cheap and worth it.