Here is the entire code;

#include <iostream>
#include <sstream>
#include <cstdlib>

using namespace std;

const int MIN_SCORE = 0;
const int MAX_SCORE = 300;
const int numofgamesinseries = 3;
const int numofplayersonteam = 4;

void printintromessage ();
void getUserInput(char& Y);
int getInt(const string &, int minValid, int maxValid);

typedef struct 
{
  int score[numofgamesinseries];
} 

  player_t;

int main(int argc, char *argv[]) 
{
    player_t players[numofplayersonteam];
    char Y;
    int k = 1;
    int l = 1;
    double seriesScore, avg;
    stringstream prompt;
    int i;

    printintromessage();
    getUserInput(Y);
    
    do 
       {
        
        if (Y == 'Y' || Y == 'y') 
         {
            cout <<"Enter scores for team " << k++ << endl;
            for (int j = 0; j < numofplayersonteam; j++) 
            {
                seriesScore = 0;
                for (i = 0; i < numofgamesinseries; i++) 
                {
                    prompt.str("");
                    prompt << "Enter player " << j+1 << "'s score " << i+1 << ": ";
                    players[j].score[i] = getInt(prompt.str(), MIN_SCORE, MAX_SCORE);
                    seriesScore += players[j].score[i];
                }
                cout << "Player " << j+1 << ":" << endl;
                for (i = 0; i < numofgamesinseries; i++) 
                {
                    cout << ". Game " << i+1 << " : " << players[j].score[i] << endl;
                }
                cout << ". Series : " << seriesScore << endl;
                avg = seriesScore / numofgamesinseries;
                cout << ". AVG : " << avg << endl << endl;
            }
        
            cout << "Team " << l++ << " Totals" <<  endl;
            cout << "Game 1 : " <<   << endl;
            cout << "Game 2 : " <<  << endl;
            cout << "Game 3 : " <<  << endl;
            cout << "Series : " <<  << endl;
            cout << "AVG : " <<  << endl;
             
               
        }
        else 
        
        {
            cout << "All finished ? Thank you !" << endl;
        }
        getUserInput(Y);
    } 
    while ((Y == 'Y' || Y == 'y'));

    return EXIT_SUCCESS;
}

int getInt(const string &prompt, int minValid, int maxValid) 
{
    stringstream ss;
    string line;
    bool inputOk = false;
    int n;

    cout << prompt;
    do {
        getline(cin,line);
        ss.clear(); ss.str(line);
        if ((!(ss >> n)) || (ss.good()) ||
                (n < minValid) || (n > maxValid)) {
            cout << endl << "That is not a valid score! score must be from "
                      << minValid << " to " << maxValid << " "
                      << endl << "Re-enter please: ";
        } else {
            inputOk = true;
        }
    } while (inputOk == false);
    return n;
}

void printintromessage () 
{
    cout << "This program processes bowling scores." << endl;
    cout << "The user is asked to enter "
              << numofgamesinseries << " bowling scores" << endl;
    cout << "for each person on the team. There are "
              << numofplayersonteam << " people" << endl;
    cout << "per team. After all the scores are entered" << endl;
    cout << "for a player, the program will list the individual" << endl;
    cout << "game scores,the player's total score (series), and" << endl;
    cout << "the player's average.After each team's input is complete," << endl;
    cout << "the program will list the team's total scores by game," << endl;
    cout << "the team's total score (series)and the team's average." << endl;
    cout << "The user will then be asked if he/she wants to" << endl;
    cout << "enter more data. If not, the program will list the" << endl;
    cout << "team with the highest total score (series) and that " << endl;
    cout << "total. If the user wants to enter more data," << endl;
    cout << "the above process is repeated." << endl;
    cout << " " << endl;
}

void getUserInput (char& Y) 
{
    string in;

    cout << "Do you want to enter (more) data?" << endl;
    cout << "Enter Y to continue, anything else to quit: ";
    getline(cin,in);
    Y = in[0];
    cout << " " << endl;
}
do 
       {
        
        if (Y == 'Y' || Y == 'y') 
         {
            cout <<"Enter scores for team " << k++ << endl;
            for (int j = 0; j < numofplayersonteam; j++) 
            {
                seriesScore = 0;
                for (i = 0; i < numofgamesinseries; i++) 
                {
                    prompt.str("");
                    prompt << "Enter player " << j+1 << "'s score " << i+1 << ": ";
                    players[j].score[i] = getInt(prompt.str(), MIN_SCORE, MAX_SCORE);
                    seriesScore += players[j].score[i];
                }
                cout << "Player " << j+1 << ":" << endl;
                for (i = 0; i < numofgamesinseries; i++) 
                {
                    cout << ". Game " << i+1 << " : " << players[j].score[i] << endl;
                }
                cout << ". Series : " << seriesScore << endl;
                avg = seriesScore / numofgamesinseries;
                cout << ". AVG : " << avg << endl << endl;
            }
        
            cout << "Team " << l++ << " Totals" <<  endl;
            cout << "Game 1 : " <<   << endl;
            cout << "Game 2 : " <<  << endl;
            cout << "Game 3 : " <<  << endl;
            cout << "Series : " <<  << endl;
            cout << "AVG : " <<  << endl;

My problem is specifically in the 2nd posted code; I'm not sure how to properly print the contents of the array, what I want it to do is take all 4 players game 1 and add them and print then game 2, game 3 etc.. how would I do this???

Create another series of loops similar to your input loops. Just convert them to output and perform the necessary arithmetic operations inside them.