The One Power, known as the Source to some, is divided into male and female halves- Saidin and Saidar respectively. Saidin and Saidar are both "woven" (or "spun" in the terminology of those from the Age of Legends) into 'weaves', using "flows" or "threads" consisting of one (or a mixture) of five elements: Earth, Water, Air, Fire and Spirit. Men are generally stronger with Fire and Earth, while women are generally stronger with Air and Water; strength in Spirit is typically equal, and equally rare. Male channelers, in general, are capable of holding more of the Power than female ones, while women generally are more dexterous in weaving the Power.
Female channelers can tell when other women are touching the Source: a white glowing aura appears around their body, though only visible to those trained to touch the One Power. Men, on the other hand, can only sense intuitively when another man is channeling (and roughly how much of the power they are wielding). Male channelers can sense a woman holding Saidar as goose bumps on their skin; women have no innate method of sensing male channeling. Both male and female channelers can sense another channeler (of the same gender, and males can sense female channelers as well) from several rooms away, and what rough direction the channeling is coming from. So, when practicing your weaves, it is probably a smart idea to do so in an isolated area.
In the current age, the Dark One's taint on Saidin causes any male with "the spark," whether or not he learns to channel safely, to inevitably go mad and succumb to a wasting sickness which causes the sufferer to rot alive (these curses may come in either order, or concurrently, at varying speeds for each male channeler). The taint came into being at the end of the Age of Legends, when Lews Therin Telamon and the Hundred Companions (actually 113 male channelers) re-sealed the Dark One into his prison, but not before the Dark One caused Saidin to become tainted. This act drove all those attempting to seal him immediately and irrevocably insane, and gradually all other male Aes Sedai fell victim to the same madness. The ensuing chaos and destruction caused the Breaking of the World or the Time of Madness.
The One Power is extremely dangerous even to those who are not destined to go mad- female channelers- and more so for the few male channelers alive in the current age. It is highly addictive, to a point where after a certain amount of channeling too long, a person can become completely anesthetized to the world and will waste away. One of the dangers is burning out. Burning out is when a channeler tries to do more than he or she can, and ends up severing themselves from the One Power. It can happen in many different ways, but the most common is attempting a weave that they are not ready for yet. Channelers who can control some extent of the One Power by themselves are called Wilders- males are automatically all Wilders- but there is always a place a female channeler can go to in order to learn. The White Tower, a school of sorts where women go to learn to channel, and eventually some become Aes Sedai.
There are two ways to learn new weaves- having someone teach you ICly, or experimenting for them. Experimentation can be a rewarding, but mostly frustrating process. On the other hand, having someone ICly teach you can be very good, since you can learn weaves that you couldn't have experimented for- you can only experiment for weaves that are at or below your strength level, but you can learn most weaves from observation. Joining the White Tower would be a good idea, although you may not learn so many combat weaves.
Some good information which is helpful for experimentation can also be found at a list of weaves