Reading a csv file into a HashMap<String, ArrayList<Integer>>

You are close

String columns[] = line.split("\t");
if (!words.containsKey(columns[1])) {
    words.put(columns[1], new ArrayList<>());
}

should be

String columns[] = line.split("\t");
String key = columns[0];                // enhance readability of code below
List<Integer> list = words.get(key);    // try to fetch the list
if (list == null)                       // check if the key is defined
{                                       //   if not
    list = new ArrayList<>();           //      create a new list
    words.put(key,list);                //      and add it to the map
}
list.add(new Integer(columns[1]));      // in either case, add the value to the list

In response to the OP's comment/question

... the final line just adds the integer to the list but not to the hashmap, does something need to be added after that?

After the statement

List<Integer> list = words.get(key);

there are two possibilities. If list is non-null, then it is a reference to (not a copy of) the list that is already in the map.

If list is null, then we know the map does not contain the given key. In that case we create a new empty list, set the variable list as a reference to the newly created list, and then add the list to the map for the key.

In either case, when we reach

list.add(new Integer(columns[1]));

the variable list contains a reference to an ArrayList that is already in the map, either the one that was there before, or one we just creatd and added. We just add the value to it.

I should add the first column is the value and the second column is the key.

You could remplace the ArrayList declaration by a List declaration. But it is not very problematic.

Anyway, not tested but the logic should be such as :

    while ((line = in.readLine()) != null) {
      String columns[] = line.split("\t");
      ArrayList<Integer> valueForCurrentLine = words.get(columns[1]);

      // you instantiate and put the arrayList once
      if (valueForCurrentLine==null){
          valueForCurrentLine = new  ArrayList<Integer>();
          words.put(columns[1],valueForCurrentLine);
      }

      valueForCurrentLine.add(columns[0]);

Upvote to Jim Garrison's answer above. Here's a little more... (Yes, you should check/mark his answer as the one that solved it)

import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class WordNet {

    private final Map<String, List<Integer>> words;
    private final static String LEXICAL_UNITS_FILE = "src/net/bwillard/practice/code/wn_s.csv";

    /**
     * 
     * @throws FileNotFoundException
     * @throws IOException
     */
    public WordNet() throws FileNotFoundException, IOException {
        words = new HashMap<>();
        readLexicalUnitsFile();
    }

    /**
     * 
     * @throws FileNotFoundException
     * @throws IOException
     */
    private void readLexicalUnitsFile() throws FileNotFoundException, IOException {

        BufferedReader in = new BufferedReader(new FileReader(LEXICAL_UNITS_FILE));
        String line;

        while ((line = in.readLine()) != null) {
            String columns[] = line.split("\t");
            String key = columns[0];
            int valueInt;
            List<Integer> valueList;

            try {
                valueInt = Integer.parseInt(columns[1]);
            } catch (NumberFormatException e) {
                System.out.println(e);
                continue;
            }

            if (words.containsKey(key)) {
                valueList = words.get(key);
            } else {
                valueList = new ArrayList<>();
                words.put(key, valueList);
            }

            valueList.add(valueInt);
        }

        in.close();
    }

    //You can test this file by running it as a standalone app....
    public static void main(String[] args) {
        try {
            WordNet wn = new WordNet();
            for (String k : wn.words.keySet()) {
                System.out.println(k + " " + wn.words.get(k));
            }
        } catch (IOException e) {
            e.printStackTrace();
        }
    }
}