Q: I have a 401(k) plan at work. Am I still able to contribute to a Roth IRA?
Roth eligibility has nothing to do with whether you have access to an employer's retirement plan or not. This only matters if you want to use a traditional IRA.
In order to contribute to a Roth IRA, your income must be under a certain threshold. If you are married and file a joint tax return, your adjusted gross income (AGI) must be $189,000 or less to make the maximum Roth IRA contribution, which for 2018 is $5,500 if you're under 50 or $6,500 if you're 50 or older. If your AGI is greater than $189,000 but less than $199,000, you may be able to make a partial Roth contribution. And if your AGI is $199,000 or higher, you can't contribute to a Roth IRA at all.
If your tax filing status is single, head of household, or married filing separately and you didn't live with your spouse, the thresholds are $120,000 for a full contribution and $135,000 for the complete phase-out. If you are married filing separately and you lived with your spouse at any point during the year, the thresholds drop to $0 and $10,000.
If you earn too much to contribute directly, there's a work-around known as the "backdoor method." Basically, there's a loophole that says that anyone, regardless of income, can convert a traditional IRA into a Roth IRA. So you could potentially contribute to a traditional IRA and immediately convert the account into a Roth IRA if that's what you want to do.