Hi Sonam, 

here is the script and controller.

When clicking the button "add competition" i would like it to create a new record in object "new test competition" which then is shown in the related list on Accounts.
The records shown on the page are already existing accounts but can be competition as well (if that makes sense)

thank you for your help!!

<apex:page  controller="AccountSelectClassController"  sidebar="false">
    <script type="text/javascript">
        function selectAllCheckboxes(obj,receivedInputID){
            var inputCheckBox = document.getElementsByTagName("input");
            for(var i=0; i<inputCheckBox.length; i++){
                if(inputCheckBox[i].id.indexOf(receivedInputID)!=-1){
                    inputCheckBox[i].checked = obj.checked;
                }
            }
        }
    </script>
    <apex:form >
        <apex:pageBlock >
            <apex:pageBlockButtons >
                <apex:commandButton value="Add to Competition" action="{!processSelected}" rerender="table2"/>
            </apex:pageBlockButtons>
 
            <apex:pageblockSection title="All Accounts" collapsible="false" columns="2">
 
                <apex:pageBlockTable value="{!wrapAccountList}" var="accWrap" id="table" title="All Accounts">
                    <apex:column >
                        <apex:facet name="header">
                            <apex:inputCheckbox onclick="selectAllCheckboxes(this,'inputId')"/>
                        </apex:facet>
                        <apex:inputCheckbox value="{!accWrap.selected}" id="inputId"/>
                    </apex:column>
                    <apex:column value="{!accWrap.acc.Name}" />
                    <apex:column value="{!accWrap.acc.BillingState}" />
                    <apex:column value="{!accWrap.acc.Phone}" />
                </apex:pageBlockTable>
 
                <apex:pageBlockTable value="{!selectedAccounts}" var="c" id="table2" title="Selected Accounts">
                    <apex:column value="{!c.Name}" headerValue="Account Name"/>
                    <apex:column value="{!c.BillingState}" headerValue="Billing State"/>
                    <apex:column value="{!c.Phone}" headerValue="Phone"/>
                </apex:pageBlockTable>
 
            </apex:pageblockSection>
        </apex:pageBlock>
    </apex:form>
 
</apex:page>

public class AccountSelectClassController {
 
    //Our collection of the class/wrapper objects wrapAccount
    public List<wrapAccount> wrapAccountList {get; set;}
    public List<Account> selectedAccounts{get;set;}
 
    public AccountSelectClassController(){
        if(wrapAccountList == null) {
            wrapAccountList = new List<wrapAccount>();
            for(Account a: [select Id, Name,BillingState, Website, Phone from Account limit 50]) {
                // As each Account is processed we create a new wrapAccount object and add it to the wrapAccountList
                wrapAccountList.add(new wrapAccount(a));
            }
        }
    }
 
    public void processSelected() {
    selectedAccounts = new List<Account>();
 
        for(wrapAccount wrapAccountObj : wrapAccountList) {
            if(wrapAccountObj.selected == true) {
                selectedAccounts.add(wrapAccountObj.acc);
            }
        }
    }