Forgive the somewhat brief response, but I'll try to offer some highlights. And I'm sorry that your father has reached that stage of life, kudos to you for taking care of some of his things.
What is your goal in disposing of the collection? Is it:
-Maximizing profit, i.e. getting as much money for it as possible?
-Disposing of it as quickly as possible, even at a lesser price?
-Seeing that it goes to a good home, where it will be appreciated and cared for?
-Something else?
You may have thought, "Well, all of those things." Unfortunately, each of those goals have better ways than others to achieve, plus various other factors will come into play.
If you want to get the most money out of it, you will likely have to sell it off in individual components on Ebay or other internet outlets such as message boards and forums. You will have to research all of the equipment, locomotives, rail cars, and anything else to determine approximate collector's value and what is a fair price. You may have relatively inexpensive "toy trains" worth only a few dollars per car, or you might have very high quality brass locomotives or rare collector's items that could be worth hundreds of dollars. Or you could have a mix, with a few gems hidden in a field of generic items.
That method will take the most effort and time. You will have to learn how to sell stuff online (if you don't already) and package and ship everything. If the collection is large, this will take years.
If you want to dispose of it as quickly as possible, look for someone that will buy the whole collection in one shot. There are some local hobby stores around the country (and a few people online) that will buy entire collections. I don't know where you are located, but if you wish this route, look for local train hobby stores in your area, call them up, explain your situation and ask if they buy collections. You won't get as good a price as the previous option, but you'll hopefully clear out everything at once.
Another option is to look for local model train shows/swap meets in your area. Circle the tables and ask the vendors if anyone is interested in buying all or part of a collection.
In a similar vein, look for a local HO model railroad club in your area. Ask if their members would be interested in buying a collection. Or if you feel magnanimous, you could consider donating it to them (they may or may not want it; if it's mostly kids' "toy train" quality, most clubs probably wouldn't be interested).
Keep in mind, all of these options require a little due diligence if you don't want to be bilked out of some value. The model railroad crowd is mostly pretty nice, but as with any collectible market, there are always some out there who will try to lowball you for what you have.
If you post some pictures of what you have (preferably clear close ups of some locomotives, rail cars, other accessories or equipment) we can give you a little bit of an idea of what you might have, i.e. a general idea of how high quality your father's collection is.
