Write a trigger to share a custom object record (Project__c) using Apex Managed Sharing (Project__Share) when a Manager__c lookup field is populated or updated.

trigger ProjectTrigger on Project__c (after insert, after update) {
    List<Project__Share> shares = new List<Project__Share>();
    Set<Id> changedIds = new Set<Id>();
    for (Project__c p : Trigger.new) {
        Id oldMgr = Trigger.isUpdate ? Trigger.oldMap.get(p.Id).Manager__c : null;
        if (p.Manager__c != oldMgr) {
            changedIds.add(p.Id);
            if (p.Manager__c != null) {
                shares.add(new Project__Share(ParentId = p.Id, UserOrGroupId = p.Manager__c,
                    AccessLevel = 'Edit', RowCause = Schema.Project__Share.RowCause.Manager__c));
            }
        }
    }
    // remove stale Apex shares first
    delete [SELECT Id FROM Project__Share WHERE ParentId IN :changedIds
            AND RowCause = :Schema.Project__Share.RowCause.Manager__c];
    insert shares;
}