Text donations to the Red Cross and others have expanded in recent years, and have become particularly prominent after natural disasters like Hurricane Sandy. The appeal, I believe, is that it's quick and allows people to give small amounts while still feeling that such amounts are appropriate. There is, however, some confusion about how much money gets to the charity and when.
The easier question is when the charity receives your donation. The funds reach the charity only after you have paid your wireless bill and the funds have been transferred to the processor (for example, mGive Foundation) and the processor then transfers it to the charity. This can take 60-90 days.
As for how much goes to the charity, the organizations involved typically stress that cell carriers waive fees so that 100% of the donation goes to charity. True, cell companies typically waive fees (though may charge you for sending a text message). This means that 100% of the donation reaches the donation processor (another charity, such as the mGive Foundation). However, these processors typically work with for-profit mobile vendors (such as mGive.com) that transmit funds from the cell company to the processor and then to the charity. These vendors do charge a fee, which can be in the range of 3%. Thus, typically less than the entire donation actually reaches the intended recipient. There are times when these fees have been waived, so this only represents the typical experience. In case this discourages you from using texting to donate, however, think of the alternatives. Credit card donations too come with their own processing fees (typically 3% or more).