State senators and reps in the state legislature are easy to meet, I've met several of each, like talked to them at Democratic party events and non partisan political/activism events around town. Told one I was voting for Bernie over Hillary when she asked. Rudely scoffed at something Clinton super delegate Bill Owen said while on stage. Happened to sit next to a former rep who was running again at a Cornel West speaking event at a college last year, they're just people. She's a retired teacher, didn't know she was a politician until I talked to her.
US Reps and Senators are more difficult, the most you can probably do without snagging an appointment months in the future is contact their office like what people been doing to express their hatred of Trump's cabinet picks. All mine are shying away from town halls and such (people have been asking) saying to make an appointment through their office.
You can pay money to attend fundraisers where they'll be, but that's garbage.