An entire industry exists to sell people a shortcut here. There is no shortcut. What there is, is a fairly short list of unglamorous things that work, and a fairly long list of things that take your money.
What actually moves it
Paying on time, every time. Payment history is the largest single factor. One missed payment undoes months. Automate the minimums so a bad week cannot cost you a year.
Keeping balances low. How much of your available credit you are using matters a great deal. Well under a third is a reasonable target, and lower is better.
Time. This is the one nobody wants. A bankruptcy stays on your report for years and its weight fades gradually. There is no way to hurry it, only ways to build good history alongside it.
Where to start with no credit at all
A secured card. You deposit a sum, that becomes your limit, and it reports like a normal card. Use it for one small recurring expense and pay it in full monthly. Check it reports to all three bureaus before you open it.
A credit-builder loan. Offered by many credit unions. You make payments into an account and receive the money at the end. It is a savings plan that generates payment history.
Being added as an authorised user on the account of someone with good habits, if a family member is willing.
What to avoid
Companies promising to “remove” accurate information — they cannot. Anyone asking for a large upfront fee. Anyone suggesting you get a new taxpayer identification number to start fresh; that is fraud, and people go to prison for it.
You have the right to dispute anything inaccurate yourself, free, in writing. That is the entire service most credit repair firms are selling.
A reasonable expectation
Many people find that with steady payment history and low balances, they are in ordinary territory within about two years, and can get a sensible mortgage rate some time after that. That is slower than anyone wants and faster than most people fear.
The bigger point
The goal is not a number. It is never being in this position again — which has more to do with an emergency fund and honest household budgeting than with a score. A financial counsellor is more useful here than a credit repair firm, and usually cheaper.