GS/RS Oil Change
This is old info but pretty much the same. Back then there was no SE so that is not included in these instructions, sorry.
The oil change on the Spyder is pretty easy other than taking the panels off to get to everything. If you're changing oil for a living on the Spyder I'm sure you could cut a few corners on the panel deal but I did it by the book the first time and that may be the best way to do it without making a big mess.
So when do you need to change the oil on the Spyder?
The book says: First 1000 km or 625 miles and then every 5000 km or 3,000 miles.
Now I went a little over on my first oil change seeing it took over 800 miles just to get the Spyder back home. When I did get it changed the oil and filter looked pretty darn good. There was just a tad bit of metal on the motor drain plug and none that I could see on the filter. 
First thing you want to do is round up all your parts and get a pan to dump your oil in. I use my wife's deep frying pan but that's another story.
You're going to need
4.1 quarts for the SM and 4.5 if you change the filter in the SE. This oil change is on a SM.
" BRP XP-S 5W-40 synthetic oil P/N 293 600 039 or an equivalent motorcycle oil meeting the requirements for API service SL, SJ, SH or SG classification.
NOTICE- To avoid damaging the clutch, do not use a motor oil meeting the API service SM or ILSACGF-4 classification. Clutch slippage will occurs."
I used Lucas Synthetic 10W-40 Motorcycle oil on this oil change. I'm sure Amsoil or even Mobil One for Motorcycles will work fine too as long as they meet those ratings.
So now that you got your oil and oil pan you're going to need a oil filter, o-ring and some crush washers. I know I'll most likely take a beating for this but more times than not I just re-use the washers and in this case the O-ring. If you got new ones use them, if not I wouldn't be too concerned about using the old ones as long as they're not damaged and they don't leak when you get done. By the way BRP says to NEVER use the sealing washer a second time so if you do have an issue it's on you.
Here's the part numbers if you want to get them from your dealer.
OEM Filter 420956745- 1 needed
O-ring 420650500- 1 needed
Crushwasher motor-420250640
Crushwasher tank-705500506
The first thing you want to do is make sure the Spyder is warm, if it's hot you need to let it cool a bit before pulling any drain plugs.
You can do this with the Spyder sitting on the ground but I like having a little room when I work under things so I went ahead and jacked it up and put it on stands to give me a little more room to work.
The next thing you want to do is start pulling body panels. You can see how to do that on page 72 of your Operator's Guide that came with the Spyder.
1- Remove left middle side panel- page 72
2- Unlatch and lift seat
3- Remove top left side panel above oil reservoir- page 73
4- Remove left rear side panel below seat- page 74
(Note) You can leave the turnsignal light hooked up if you want. That's what I did.
5- Remove the lower side panel below oil reservoir- page 74
6- Remove bottom plate that's under the oil filter
7- Clean drain plugs before removing.
8- Place drain pan under oil reservoir and remove plug. Unscrew and remove dipstick so all the oil can drain.
Reservoir Drain Plug
9- After all the oil has drained from the reservoir install drian plug with new washer if you have one.
10- Place drain pan under drain plug on motor.
11- Remove engine drain plug and allow the oil to drain completely from crankcase. Remove any metal shavings from drain plug magnet.
12- After all the oil has drained from the crankcase install drian plug with new washer if you have one.
Crankcase drain plug
13- Remove two screws from oil filter cover
14- Remove oil filter cover with O-ring
15- Remove oil filter and replace with new one and new O-ring if you have one
16- Install oil filter cover with new filter and O-ring back on motor. Make sure you seat the new filter in the cover first and then install the cover.
17- Add three quarts of new oil to oil reservoir and install dipstick.
18- Wipe down any oil on motor or reservoir.
19- Check to make sure all drain plugs are tight and that oil filter cover is tight.
20- Start the motor and let warm up and check for oil leaks after warm.
21- Add one quart of oil to reservoir and check oil level.
22- If all is well reinstall body panels and go for a ride. Check again for oil leaks after ride.
Hope this helps to take some of the guess work out of doing your own oil and filter change and if you have any questions let me know.