A. WAYS TO RACK FROM JUST ABOUT ANYTHING:
This is the simplest way to start a siphon- hence you may want to skip this. You can either just suck on the (soon to be) discharge end racking hose, or, if sanitation concerns you, put a short length of large diameter tubing over the end, suck on that and then remove it before the beer touches it. It really helps a lot if you use a clear and a longer than needed racking hose. Clear so you can see the liquid filling the hose as you suck and can thereby remove your mouth or the large tubing from the end of the hose before the beer touches it and longer so you can have the end above the level of beer in the carboy and thereby enable you to keep it free of beer. A valve located towards the discharge end of the racking hose is highly desirable although kinking the hose shut can also work. The valve allows you to lower the end of the hose into whatever you're racking to without the beer gushing out. The vlave and lon racking line also serve another purpose too. Sometimes you'll find a plug of air trapped in the "U" of the hose that's formed at the top of the container being racked from. This plug of air can prevent the siphon from working. The remedy is to open the valve, lower the end of the hose until beer is almost to the valve, shut the valve (to trap the beer in the line, raise the hose and it's end above the level of beer in the container being racked from and then open the valve (but be ready to shut it quickly!). The air will be forced out by the slug of beer in the hose beer. Close the valve when all the air is expelled. There's no free lunch, so, the downside to this is you're oxygenating the beer a bit.
2. Use a Fuel
Not, not one removed from that '72 Pacer on cement blocks in your yard :-) The fuel pump I mean is one of those black bulb type affairs that are used in the fuel line between and outboard boat motor and the fuel tank. They a have check valve at both ends so all you have to do is sanitize it (Iodophor is recommended), connect it in the racking line (observe flow arrows!) and squeeze it to start. Sometimes the check valves don't seal well, so try shaking the pump and holding it vertical- with the arrows pointed up. If it still doesn't suck well, put a clamp type valve in the racking line downstream of the valve, open the valve (or kink the line), squeeze the pump (hold it squeezed), close the valve then release your squeeze. Repeat as needed. Before the first use, run warm water thru the valve for awhile then taste and smell a sample of the water to ensure the bulb won't make your beer rubbery tasting.
the Racking Tubing with Water
To me this is a hassle and is messy, but I'll throw it out anyway. The idea is to fill the racking tube and hose with water, close off the discharge end (which traps the water in the line), stick the cane in the container your racking from, put the other end into the container you're racking to then open end of the hose. A clamp on type valve in the hose works well.
B. WAYS TO RACK FROM A CARBOY
1. Use Pressure
Insert a plastic racking cane into the large hole of one of those orange soft plastic carboy caps. Applying a bit of keg lube will help and will make adjusting the depth later while you're racking a breeze. I use 7/16" OD x 5/16" ID vinyl tubing with the cane. Info on how to fit it to the cane is here. Put the cap/cane on the carboy with liquid to be racked and CAREFULLY pressurize the carboy via the smaller opening in the orange cap. This will force the liquid up into the racking cane. I've blowing into carboys with beer in them a couple of times without noticably contaminating the brews. If contamination concerns you enough, pressurizing via a HEPA filter / filter holder should work. Althought I've done it, I do NOT recommend using a higher pressure source (e.g., a gingerly pumped bicyle air pump) since one could turn the carboy into a hellva glass grenade if the racking line was somehow plugged (e.g.- one forgot to open the valve in it) and the blow-off pressure of the orange cap was greater than the rupture pressure of the carboy. I've not found a suitable and safe low pressure source- a ballon, the kids pump type ballon inflator and a typical, cheap aquarium pump don't have enough pressure. A co2 cylinder with its regulator set to 0 psig and slowly increased seems like a good idea, but, what happens if the regulator screws up. It's too risky for me...
to a Second Carboy
Set up the full carboy as in B.1 above. Put another orange cap and racking cane on the empty carboy. Instead of pressurizing the full carboy, suck on the empty one via the smaller hole in the orange cap. WARNING: Don't try this if you've purged the empty carboy with CO2!
Fit a 1" or so lenght of 3/16" ID vinyl tubing over the liquid out disconnect. Info on how to do that is here. Slip some 7/16" OD x 5/16" ID vinyl tubing over that. Kegs can be pressurized, so CO2 via a regulator connected to the gas-in disconnect is ideal. Before connecing it to the keg, set the regulator to 0 psig and ensure there's no pressure on the keg (if there's pressure and you don't have a check valve downstream of the regulator, you could get beer in the regulator). If you don't have a co2 cylinder and regulator, a bicycle air pump works.
Racking between cornies is very easy. Start by purging the empty keg with CO2. Connect the beer-out disconnects together. Lift the relief valve on the empty keg and apply a bit of CO2 pressure to the full keg via the gas-out disconnect. Once flow starts, close the relief valve on the second keg and connect the gas-in disconnects on both kegs together with some tubing. This creates a closed system and thereby practically eliminates air touching your beer.
A TIP: If you ferment in cornies, you probably have the beer-out dip tube cut short to avoid racking off the yeast cake and/or trub. An improvement on this is to fit the red colored flow diverting tip from a racking cane to the end of the dip tube. The tip is too big to stay on the dip tube like it does on a racking cane, so take a short piece of vinyl tubing, split it lenghtwise and use it as a spacer between the red tip and the end of the dip tube.
Play around with racking water to perfect your technique.
Sometimes a bubble of air (or maybe CO2 coming out of solution with the beer) is lodged where the racking cane joins the racking hose. The bubble will slow the flow, and, if it's an air bubble, it may oxidize your beer. Get rid of the bubble by squeezing the hose partially shut as the beer is flowing. The increased velocity will sweep the bubble away.
I like those nylon "valves" that slip over and clamp down on flexible tubing. Forget about the small size model- spend a few extra cents and get the big one. Not only does the larger one provide more leverage and hence is easier to operate, it also allows you to throttle the flow.