Many annual grasses can be controlled by a pre-emergence herbicide like Preen. The herbicide acts to prevent the seeds from germinating. Also, letting your grass grow to two inches will shade out weed seeds that need sunshine to germinate.

In the case of perennial invasive grasses, there are fewer herbicide options. A general herbicide like Round-up will work as long as you avoid getting it on the good grass. I cut the bottom off of a one gallon milk container and place it over the weed. Then I insert the spray wand into the open bottle top and and spray down onto my target. I also use a weed torch and burn the top off the weed until it wears the roots out and the weed dies. The weed grows back a few times, but eventually it runs out of energy to regrow.

Here is a link to a website that can help you identify your problem grass plus recommended herbicide treatments.

Thank you for your advice.  I think that the grass is either dallisgrass or orchardgrass.  One web site I looked at recommended spraying orchardgrass with white vinegar.  Have you ever heard of this treatment?  Would vinegar kill the turfgrass?

The acid will damage green leaves on turf grass as well as invasive grass. Treatments like vinegar kill the top growth but not the roots. The crown of a grass plant is below the leaves to allow grass to recover from fire. That is the reason we can mow grass and it grows back. All treatments that kill top growth on perennial grass have to be repeated until the roots run out of energy.
You can divide most treatments that kill plants into those that kill top growth and those that are systemic like Round-up. Systemic herbicides enter the plant and flow through the transport systems, killing the entire plant. Round-up can be used to kill tree roots if it is painted directly on a freshly cut stump.
The advice of Penn State is to start with the least lethal treatment and the one most appropriate to the job. Some weeds, like crown vetch, spread when you try to dig them out because their roots have the ability to send out runners that produce new top growth, thus spreading the weed if you don't get every last bit of the root system.
Annual weeds are best treated with a preemergent herbicide because over the years annual weeds produce a lot of seeds. However once you apply a preemergent herbicide, you can't get results if you reseed your lawn with desirable grass seed.
Fertilizers and chemicals you use to control weeds, diseases, and pests can have consequences that you don't expect. Overuse can cause salts to build up in your soil and toxic runoff into nearby waterways.
The foundation of a good lawn starts with well prepared soil with a good percentage of organic material like compost. You can purchase an inexpensive soil test kit at your local Penn State extension and find out if your soil is optimum for turf grass. It will give you a prescription for what to add to the soil. You can also find out what grass species will grow best in your environment. Healthy grass plants will do the best job of crowding out weeds.
Here is a link to a Penn State publication called Lawn Management Through the Seasons.