I haven't used HOD for this (yet? I'm about to start HOD with my youngest in 7th grade), but I have graduated 2 students from homeschooling. The best quick explanation I've seen is from HSLDA. It's on their non-member section, so you can look there for their high school page.
In most states and for almost all colleges, homeschoolers can make their own diplomas and issue their own transcripts. About the time your student starts high school, look at what is required for admission to a few of the colleges you think your student might attend. It doesn't have to be extremely specific, but it's good to look at a state school and a private school or two. If you know already about an interest in a highly selective college like Cal Tech or an Ivy League school, then definitely check with them as well. You will find a pretty standard list, usually 4 years of English, 3 years of math, 2-3 years of science, and about 2.5 years of socials studies. Some places do require more though. (If you live in CO, eg, U. of CO requires 4 years of math.) These requirements can change over time, so there's not a lot of point worrying if your oldest is 5yo.
Some schools have other requirements, such as the state university which one of my kids applied to--they accepted her application but said she would need to take 2 semesters of foreign language if she didn't finish 2 years of them in high school.
There are very few situations which require a GED (some state colleges in NY require them, from what I have read), and a few situations where it's pejorative, such as going into the military. In almost all cases, you issue the diploma and make a transcript, and it's good. It helps if you have test scores that back up your claims. Eg, if you claim your child has done honors courses, they'd better get pretty good scores on SAT/ACTs.
The only generally difficult thing to do without accredited course work is to put a teen into a public high school after 9th grade. It's easier to get into Harvard than to accomplish this feat! There are a few cases, more lately that I've heard of, where a public school was willing to accept homeschool credits towards graduation, but many simply reject them out of hand. In that case, you might be forced to finish via homeschooling, to use a private school, or to simply skip into community college. None of these are extremely bad options, in most cases, so I have never worried about it.
A transcript needs to made for each year from 9th grade onwards, and dual enrollment courses count double--1 semester college course = 1 year high school course. You will put all their courses, including CC courses, under each year of schooling, and then total up units and grade points. The HSLDA website will talk you through some of the options of how to count units, calculate GPAs, etc. (I can also do it if you want me to me that specific. It's not extremely difficult, but does have several steps.)
If your children do finish a full AA at the community college, it makes transferring easier, but it can also be done without that. My kids had 20 units and 8 units, and had no trouble. Since the courses are done before the end of high school, they are still considered freshmen when they come in, and qualify for freshman scholarships instead of transfer ones. The freshman ones are usually significantly better, and one of my kids got a National Merit scholarship. The other has 1/2 tuition at her Christian college. My oldest had 20 units, and will finish after 3 years there. My 2nd has the National Merit but had only 8 college units and is taking honors courses, so she will be there the full 4 years.
It is possible to pay someone a great deal of money (NARHS was $450 per year, last I checked, don't know what Abeka costs) for an accredited diploma, but it's really not necessary. The vast majority of colleges, including state universities, private colleges both Christian and secular, and Ivy League schools, like homeschoolers and will accept them at rates similar to or higher than public school kids. My kids got into every school they applied to with at least 1/2 tuition scholarships offered to them. They did have very good SAT/ACT scores, but it was not hard to get them in.
Does that all make sense? I'm glad to answer more questions if anyone has them, and there are probably others here who have done it, too.