As far as I get the question, there are no such structure as **WHERE 1** in apex.
Based on your question, next structure may be used:


    List<String> and_conditions = new List<String>();
    //add some condition like/
    //  and_conditions.add( ' test__c = true AND test_data__c != null ');
    //  and_conditions.add(' test__c = false AND test_data__c = \'Data\' ');
    String where_clause = ' ';
    if (!and_conditions.isEmpty()){
        for(Integer i = 0; i < and_conditions.size(); i++){
             if(i == 0){
                 where_clause = ' WHERE (' + and_conditions.get(i) + ') ';
             }else{
                 where_clause +=' AND (' + and_conditions.get(i) + ') ';
             }
        }    
    }

That would support only AND clause as a root clause, but that is simple enough to understand pattern, and improve it on demand.

P.S. there are some statements which are always true. Like **WHERE Id != null**

P.S.S. With 1.5 year more experience, code written above can be improved

    List<String> and_conditions = new List<String>();
    //add some condition like/
    //  and_conditions.add( ' test__c = true AND test_data__c != null ');
    //  and_conditions.add(' test__c = false AND test_data__c = \'Data\' ');
    String where_clause = ' ';
    if (!and_conditions.isEmpty()){
        where_clause = 'WHERE (' + String.join(and_conditions, ' ) AND ( ') + ')';
    }