One of the "easier" things about getting into an SLP program is that you don't have to be an undergrad major in communication disorders (even thought I'm sure that helps). Most graduate slp programs have about 7-10 prerequisite classes you need to take to be considered for admissions. The good thing is that these prerequisites are more or less the same for most schools out there (including phonetics, anatomy of speech and hearing systems, intro to disorders, intro to audiology). You can take the pre-reqs in as many schools as you need to, as long as you take all the ones that the program you are applying to requires. You'll also need recommendations, and probably will need to take the GRE.
Check
www.asha.org; it has a section where you can look up schools by state. They should have a link to the school's admissions place and you can find the prerequisits. I do know that New York Medical College's School of Public Health SLP program does not require any speech pre-reqs. Getting into a program is not too easy as you need around a 3.5GPA and probably want to have high grades in your pre-reqs.
After you graduate, you have to do 9 months of a clinical fellowship aka CFY (clinical fellowship year). This is you going out there looking for a job and getting hired (yes, you'll be getting a paycheck) and working under supervision (not over your shoulder - about 25% of the time). Why 9 months? ASHA requires a certain amount of after-graduating-working-under-supervision hours to allow you to practice on your own. 9 months = full time 35ish hours a week (if you want to part-time there are separate rules where you have to work no less than a certain amount of hours per week). I'm not sure if 9 months applies to all 50 states, but it's around that time frame. You also have to take the PRAXIS test. After that you get your license and CCCs (but that's all the way down the road)
The career outlook is good and will probably stay this way. If you enjoy and are comfortable working with children ages 0 - 3 and are creative, this field will give you lots of dollars.
I would say this: before deciding to get on the path to be a speech pathologist, make sure this is really what you want to do. Observe, shadow, volunteer for, stalk (ok, maybe not that one) a speech pathologist in as many settings as possible for as long as allowed (including hospitals, nursing homes - as observing an SLP who works with kids will probably be easier) to get a complete understanding of what an SLP does/doesn't do. Make sure you really, truly, fully understand what a speech pathologist does for a living and decide that this really is the field for you. If you don't have the complete picture and decide to go into this field, chances are you could be pretty miserable (especially if you are going into it thinking that speech pathology is based in concrete evidence-based science - I would say 50% of it isn't). I'm not saying being an SLP is bad; I'm just saying that this is one of those careers that unless you love it, you'll hate it.