There are lots of low cost mutual/index funds that need minimums of < 250, just not many (or maybe any) at Vanguard. Check out Fidelity or Schwab on their website, and look at their fund screeners (maybe google for that term directly, e.g. [brokerage] fund screener) and see if the $ minimum is a screening option. From there you can easily sign up online, or call them up and have them walk you through the process - they're very friendly and helpful as they want your business. The one thing I'd note is that it is typically best in my opinion to buy a family's fund through their own house as sometimes there are other charges involved, though I think that is mostly for ETFs and such. By that I mean you could buy e.g. Vanguard ETFs/Mutual funds/Index funds commission free through Vanguard but may have to pay a fee if you go through another broker, same for Schwab funds at Schwab etc. These would be good things to ask on the phone or here if you have questions. Those screeners might help you find what index fund(s) you want to set her up in. Use these tools to pick what fund(s) you want to buy into, and from there you should be able to sign up online using an email address and can buy online if you link a bank account. Or you can call the place up and they'll create an account for you and walk you through the process.
Depending on her saving ability and goals, it may make sense to save up until she can get into the fund she really wants to be in if it has a minimum of 1,000 or 3,000 or something. Possibly easier to do that than get into one fund and then sell and move later, especially if she's wary of the process and you want to make it easy for her (I'm not at all wary so I'd just get started as soon as possible but everyone is different). If her income level will allow it, and the limits are easy to look up online but I think the maximum salary to be eligible for straight (not backdoor) Roth is something like 87,000, I'd suggest putting money into an IRA or more probably Roth IRA for a few reasons. That might help by giving her a goal to reach by the end of the year as a first start. That'll also allow her to move between funds if she changes her goals, or into funds with larger minimums without tax implications (if you are doing this, and especially x10 if you want to move brokers as part of this process, if you are at all unsure what you are doing I strongly recommend calling and having this done over the phone so you don't do something like take a distribution and get a penalty. A moderately easy thing to fix at tax time, but easier to make sure it is done right at the start. If you do decide you want to change houses, call up the place you are going and they will usually handle everything including contacting the other broker and forms etc. as again they want your business.
Here is the screener for schwab, for example:
http://www.schwab.com/public/schwab/investing/investment_help/investment_research/mutual_fund_research/mutual_funds.html?path=%2FProspect%2FResearch%2Fmutualfunds%2Foverview%2Fscreener.asp%3Fsymbol%3DFidelity:
https://www.fidelity.com/fund-screener/research.shtmlVanguard:
https://personal.vanguard.com/us/FundsMFSBasicSearch?FROM=VANIf those screeners aren't helping you out, you can always call them up and say "I want a total stock market index fund with a minimum of $250 or less. What do you have to offer me? what is the expense ratio? tell me every single fee involved," and go from there. Good luck.
One other small thing I've used in the past to encourage or explain what saving money means is to do some math to show people 2 things:
1. If you save x dollars you'll be able to get this every year/day/month
forever, for free (using the 4% rule) - works great for small purchases like 1 pizza a week. E.g. to get 1 $5 pizza a week, every week, sustainable indefinitely "for free" (without using any of your principal) you'd need to save and invest $5*52*25=$6,500. Make sure they don't start actually withdrawing to do this once they've saved enough though, and use cashflow instead =).
2. If you delay this purchase by x years and invest instead you'll be able to get y.y of these / get 1 of these and have $zz left over - works great for big purchases. "What if someone paid you $8,000 to wait three years to buy that car/boat?"