What affect would adding my 19 year old sister have on my return?

Taxes are complicated and simple answers are usually not possible.  You can use this tool to do an estimate https://turbotax.intuit.com/tax-tools/calculators/taxcaster/?s=1.

That said; assuming you have a tax liability, claiming another dependent would save you $4050 (a dependent’s exemption) times your marginal tax bracket (e.g. $4050 x 15% = $608)*.

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit and/or student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income. They are interrelated but the rules are different for each.

Since your sister is not full time student, over 18, she  cannot be a QC. A person can still be a Qualifying relative dependent, if not a Qualifying Child, if he meets the 6 tests for claiming a dependent:

1. Closely Related (sister qualifies) OR live with the taxpayer ALL year

2. His/her gross taxable income for the year must be less than $4,050 (2016)

3. The taxpayer must have provided more than 1/2 his support

In either case:

4. He must be a US citizen or resident of the US, Canada or Mexico

5. He must not file a joint return with his spouse or be claiming a dependent of his own

6. He must not be the qualifying child of another taxpayer

*If your sister also qualifies you for Head of Household filing status, that would result in additional tax savings.