How can I randomly select one element from a vector or array?

You want the rand crate, specifically the choose method.

use rand::seq::SliceRandom; // 0.7.2

fn main() {
    let vs = vec![0, 1, 2, 3, 4];
    println!("{:?}", vs.choose(&mut rand::thread_rng()));
}

Another choice for weighted sampling that is already included in the rand crate is WeightedIndex, which has an example:

use rand::prelude::*;
use rand::distributions::WeightedIndex;

let choices = ['a', 'b', 'c'];
let weights = [2,   1,   1];
let dist = WeightedIndex::new(&weights).unwrap();
let mut rng = thread_rng();
for _ in 0..100 {
    // 50% chance to print 'a', 25% chance to print 'b', 25% chance to print 'c'
    println!("{}", choices[dist.sample(&mut rng)]);
}

let items = [('a', 0), ('b', 3), ('c', 7)];
let dist2 = WeightedIndex::new(items.iter().map(|item| item.1)).unwrap();
for _ in 0..100 {
    // 0% chance to print 'a', 30% chance to print 'b', 70% chance to print 'c'
    println!("{}", items[dist2.sample(&mut rng)].0);
}

Using choose_multiple:

use rand::seq::SliceRandom; // 0.7.2

fn main() {
    let samples = vec!["hi", "this", "is", "a", "test!"];
    let sample: Vec<_> = samples
        .choose_multiple(&mut rand::thread_rng(), 1)
        .collect();
    println!("{:?}", sample);
}

If you want to choose more than one element then the random_choice crate may be right for you:

extern crate random_choice;
use self::random_choice::random_choice;

fn main() {
    let mut samples = vec!["hi", "this", "is", "a", "test!"];
    let weights: Vec<f64> = vec![5.6, 7.8, 9.7, 1.1, 2.0];

    let number_choices = 100;
    let choices = random_choice().random_choice_f64(&samples, &weights, number_choices);

    for choice in choices {
        print!("{}, ", choice);
    }
}