So, you are talking about an OTB blitz tourney? Rated or unrated? If rated then the first order of business is either starting an affiliate or finding one to sponsor the tourney and becoming a TD or finding one to run it.
Usually one of the biggest worries is finding a good location that doesn't cost too much. Then, if rated, put in a TLA in Chess Life (will cost some money) or if you want to go free, you can get it posted on the online-only TLA section. Get the event posted to the state affilate website and if you are close enough for bordering states, on their websites if they will allow it (and if they do it free or cheap). Also, do it in advance, preferably 3 months or more if you can.
You can also advertise in local papers.
If you are going unrated, then it makes thing a little easier.You can still look to see if you can find an affiliate to sponsor the event but overall costs can be kept down and you will still want to advertise in a similar method.
There are probably more good ways, but a lot depends on how many players are in your area and how willing players are to travel if they are not. Where I live there aren't a ton of players that attend tourneys. I usually pull between 15-20 players to events, but I'm also not the best with advertising.
Hey there chess.com, I am writing to ask you what the best way to start a Blitz chess tournament would be? I live in a very remote place where there aren't any tournaments nearby. The nearest one I played in was Galloway NJ at the BoardWalk Open and even then it cost me. I will honestly say I didn't do well in that tournament and I know why. High school tournaments in school are not the same as the USCF rated tournaments outside of it. Unfortunate right? Anways, I am thinking about starting a small blitz tournament in my town as a sort of charity tournament. Any ideas on how I could arrange this? How to attract people to it? I need a bit of advice. Anyways, thanks and if you want a game or two, or 10, or 40, or 1,000 then hit me up with a message :D.