I would use Unitys PlayerPrefs System.

Example:

Setting Score:

public Text score;
int currentscore = 0;

Increasing Score:

currentscore += 1;
score.text = currentscore.ToString();

Setting HighScore and Loading Menu:

GameManager.SetHighScore(currentscore);
SceneManager.LoadScene("Menu");

Functions to Load/Change PlayerPrefs:

void Start()
{
    highscore.text = PlayerPrefs.GetInt("HighScore", 0).ToString();
}

public static void SetHighScore(int score)
{
   if (score > PlayerPrefs.GetInt("HighScore", 0))
   {
       PlayerPrefs.SetInt("HighScore", score);
   }
}

Your Code adapted to PlayerPrefs:

public int currentSpears = 0;

public GameObject rune1;
public GameObject rune2;
public GameObject rune3;

void Start()
{
    currentSpears = PlayerPrefs.GetInt("CurrentSpears", 0).ToString();
}

public static void IncreaseSpears()
{
    int spears = PlayerPrefs.GetInt("CurrentSpears", 0);
    PlayerPrefs.SetInt("CurrentSpears", spears++);
}

public void RuneCollection()
{
    if (currentSpears >= 2)
    {
        Debug.Log("3 runes collected!");
        rune3.SetActive(true);
        totalRunes = 3;
    }
    else if (currentSpears >= 1)
    {
        Debug.Log("2 runes collected!");
        rune2.SetActive(true);
        totalRunes = 2;
    }
    else
    {
        Debug.Log("1 rune collected!");
        rune1.SetActive(true);
        totalRunes = 1;
    }
}

You can save your data with PlayerPrefs for some single values or PersistentDataPath for some multiple values such as a class. Find out more with this link, and you can use them as below.

PlayerPrefs:

private int score = 0;

//set value
PlayerPrefs.SetInt("Score", score);

//get value
private int savedScore = PlayerPrefs.GetInt("Score");

PersistentDataPath:

private string savedName;
private int savedHealth;
private string loadedName;
private int loadedHealth;

public void Save(){
    BinaryFormatter bf = new BinaryFormatter();
    FileStream file = File.Open(Application.persistentDataPath + "/FileName.dat", 
         FileMode.Create);
    PlayerClass newData = new PlayerClass();
    newData.health = savedHealth;
    newData.name = savedName;
    bf.Serialize(file, newData);
    file.Close();
}

public void Load(){

    if (File.Exists(Application.persistentDataPath + "/FileName.dat")){
        BinaryFormatter bf = new BinaryFormatter();
        FileStream file = File.Open(Application.persistentDataPath + "/FileName.dat", FileMode.Open);
        ObjData newData = (ObjData)bf.Deserialize(file);
        file.Close();
        loadedHealth = newData.health;
        loadedName = newData.name;
    }
}

[Serializable]
class PlayerClass{
    public string name;
    public int health;

}

Im currently working on a little mobile game in which you throw spears at targets, and depending on how many spears you have left at the end of the level you get between one and three Runes (similar to the Star scoring sytem in Angry Birds). The plan is to save the runes and use them to unlock different spear variants in the Main Menu.
At the moment you can see how many runes you got after completeing the level, but the values are not yet being saved.
My question is, how would I go about saving the Runes after each Level? Any ideas? You can see the part of the script Im using for that below. Thanks in advance.

public int totalRunes = 0;

public GameObject rune1;
public GameObject rune2;
public GameObject rune3;
public void RuneCollection()
{
    if (currentSpears >= 2)
    {
        Debug.Log("3 runes collected!");
        rune3.SetActive(true);
        totalRunes = 3;
    }
    else if (currentSpears >= 1)
    {
        Debug.Log("2 runes collected!");
        rune2.SetActive(true);
        totalRunes = 2;
    }
    else
    {
        Debug.Log("1 rune collected!");
        rune1.SetActive(true);
        totalRunes = 1;
    }
}