What is the best way to categorize/group and sort a list of elements using javascript?

Something like this should get you started - the code is commented with explanations (see it in action):

// convert array of objects into a Map grouped and ordered by supplied key
function group(items, key) {
    // get unique values for grouping key
    const unique = [
        ...new Set(items.map(item => item[key]))
    ];

    // will be ascending by default
    unique.sort();

    // sorting all of the results by title field
    const sortFn = (a, b) => a.title > b.title;

    const sortItems = (val) => {
        // filters the result set to items sharing the current group field value
        let sorted = items.filter(item => item[key] === val);
        // sort by title
        sorted.sort(sortFn);
        return sorted;
    }

    // reduce to a Map (which preserves insertion order and maintains the group key sorting)
    return unique.reduce((map, cur) => map.set(cur, sortItems(cur)), new Map());
}

// testing it out
data = [{
  title: 'foo',
    category: 'book',
    year: 2016,
}, {
    title: 'bar',
    category: 'book',
    year: 2016,
}, {
    title: 'blah',
    category: 'paper',
    year: 2010,
}, {
    title: 'idk',
    category: 'paper',
    year: 2015,
}]

group(data, 'category'); // Map {"book" => [Object, Object], "paper" => [Object, Object]}
group(data, 'year'); // Map {2010 => [Object], 2015 => [Object], 2016 => [Object, Object]}

For displaying, you can use for...of with destructuring:

for (let [category, items] of group(data, 'category')) {
    console.log(`
       <div class="item">
          <h3>${category}</h3>
          <ol>${items.map(item => `<li>${item.title}</li>`).join('')}</ol>
       </div>
    `);
}

Note that even though I used ES6 throughout, this can easily be refactored to be more backwards compatible.