Draining the oil: Put the bike on the center stand and remove the drain plug. It's on the lower left front corner of oil pan. It's good to have the oil a little bit warm. Start with the bike cold, but let the engine idle for about two minutes, until one or two bars show on the temperature gauge.
Filling the oil: Remove the inspection cover from the tupperware, right panel just behind the cylinder heads. To do this take a small object, your key will do, and push the plastic retaining pin center stub in 1/8". Then the whole retaining pin will pop right out. Take the retaining pin apart. To put the retaining pin back in, put the female part into the plastic piece, then the center part last.The tupperware has a tab on the top. You'll figure it out. Now, remove the spark plug cover. It's the plastic piece about 8" long 3" wide on top of the cylinders. Pull up the back edge - it's held on with one rubber plug. Now, push the whole piece forwards 1/4". There are two little fingers on the front of the plastic piece that hook under. The oil fill is the obvious plastic knob right there. You will need a foot long funnel. Pour in 1 gallon and forget about measuring - this is correct.
The ST1300 takes four quarts of oil. To read the oil level correctly, you must start the engine and let it idle until the engine and oil are warm - three bars on the temperature gauge. Then shut off the engine, and wait three minutes for the oil to drain down to the oil pan. Read the oil level while the bike is on its center stand. The site glass for reading the oil level is on the lower right hand side of the engine, visible through a vent in the fairing lower. You'll find four quarts is correct for a simple oil change, or about 4.1 quarts if you also change the filter. If the oil level is above the high mark, remove oil as necessary.
Warning: The experience of existing ST1300 owners is that the dealers almost always overfill the oil on these bikes by anywhere from ½ quart to 1 ½ quarts. Overfilling your engine oil can result in excessive internal air pressures which can cause gaskets and seals to fail. Some ST1300s are developing oil leaks from the top end which are difficult to track down and will keep your bike in the shop for more than a month. We think these two facts may be related. I strongly urge you to check your oil level and adjust it or have it adjusted as necessary.
Get a 65mm oil filter wrench, the type that fits on a ratchet. You can get this at any auto parts store for about $4. Get a metal one, not the *!@# plastic type. Place a large flat metal pan under the bike, like a cookie sheet. This process is quite messy. Put the bike on the center stand, with the center stand legs in the middle of the cookie sheet. If your oil filter will drain onto fairing or frame parts, you can use aluminum foil to make protective shields that guide the oil to where it belongs.
Remove your old oil filter. Honda over tightens their oil filters at the factory. This has been a problem for everyone. I had to hammer a screwdriver through the original oil filter and turn it 1/8 turn to get it loose. Put a bit of oil on the O-ring of the new filter, turn it on hand tight, then use your filter wrench to tighten it a bit more, 1/2 turn is fine. You don't need or want to get anywhere near as tight as Honda does. Your Honda manual says the oil filter should be torqued to 24 foot-pounds. I consider this insane, as does every filter manufacturer in the US.
Drive chains need a few types of maintenance. It's important to keep the chain and the sprockets clean, as any dirt on your chain will likely work its way into the chain and cause wear. Modern chains are internally lubricated, and have o-rings to keep the lubricants inside. The o-rings need to be kept clean, the rubber kept fresh and moist. The side plates on the chain need some lubrication. Finally, the chain itself stretches over its life, and needs adjustment from time to time.
Put your bike on the center stand. If your rear wheel is off the bike, you can pull the sprocket assembly off the wheel. It will just pull off, it's held on by friction with the rubber dampers, there's no bolts. Put the sprocket assembly back on the chain, and put the rear axle through it. Put the motor in neutral, and you can now easily move the chain back and forth. If you don't have a center stand, you can often place a jack under the rear shock linkage and lift the bike onto the jack, side stand, and front wheel enough to spin the rear tire. A half inch of clearance from the rear tire to the ground is plenty.
This is a quite messy job. If you get some spray shaving cream and rub it into your hands and wrists, it will seal your skin and pores with silicon lubricant. Later, when you're all done, this will make cleaning up your hands a lot easier.
Use a rag saturated with WD-40. Don't use gasoline, this will ruin your o-rings. Spin the rear tire slowly while holding the rag against the outer sides of the chain to get the worst of the dirt off. You can also use the same rag to get the grease and dirt off of the rear sprocket and the wheel rim. Now, spin the wheel faster and spray WD-40 directly into the links. This will clean out the side plates and keep the o-rings lubricated and conditioned.
Finally, when the chain is clean and lubricated with light oil, you can seal the chain with a chain wax, such as Maxima or Castrol. Or, you can use Bel-Ray Super Clean chain lube, which has a very good reputation on street bikes. I don't recommend other chain lubes for street use - they seem to pick up more dirt and just make things worse.
Your owners manual will tell you how to adjust your chain. The chain should have roughly 1¼" to 1½" (30mm to 35mm) play in it halfway between the sprockets. There will likely be a colored marker on your swing arm that tells you when your chain has stretched to its useful limit.
Your swing arm almost certain has chain alignment marks on the two sides. However, these are notoriously inaccurate. Much better is to either align your rear wheel using the string method (see Rear Wheel Alignment above) or prop up your rear wheel, and spin it a few times while sighting along the chain and rear sprocket. The rear wheel is aligned when the sprocket teeth stay centered in the middle of the chain.