Alternative Powers are a true path unto madness. They are also one of my favorite parts of the game. Once you have a base power, we'll call it Blast 10, than you can choose to get alternative versions of that power. These alternative powers are considered the same power for purposes of nullification and such but represent different uses of a single base ability.
So, let's assume that your Blast 10 power is representing a projected bolt of fire. That's all well and good for attacking at range but you want to be an awesome fire juggler or something like that. So you can either get a whole new power (probably cost a ton of points) or you can spend one point for the Alternative Power feat, apply it to Blast 10, and basically make your new power!
So, you get Alternative Power and now you are working with the same number of Power Points you invested in the base power to make the new one. Blast costs 2 PP a rank so you've got a little pool of 20 PP. Keeping things easy, we'll pick a new power that's also 2 PP per rank. So we use Create Object with no frills and get Create Object 10.
Now your character can use his fire to attack (Blast) or make things with it (Create Object) but he can't do both at the same time, he has to do one or the other each round. If no frills isn't how your character normally likes to go than you can mess around with the pools for the Alternative Power. For example, if you wanted to be able to move around your flame objects with sheer will than you could apply the Movable Extra, which adds 1 to the PP cost for each rank of the power. So, instead of 2PP you pay 3PP each rank. However, that means that you can only get to rank 6 with Create Object because the original dice pool for the power is 20 and 6 ranks at 3 per is 18 points. You can't buy another becuase you'd push the total cost up to 21 and you can't go over the origianl cost. This also leaves you with 2 PP floating around you'll need to do something with. Since you can't buy a full rank you decide to get some Feats to boost the power farther. In this case, we'll go with the Progression Feat, which greatly increases the volume of objecs that you can form. One rank of that (1 PP) and one rank of the Precise Feat which will let you make very detailed objects. Now we have a toal of 20, 6 ranks at 3 per with 2 PP in Feats. Congradulations, you haban Alternative Power.
You can do this as many times with th base power as you want BUT you can still only use one power in the Array at a time.