In terms of transborder flights, if you do not want to worry about tango fares, with non-status half-miles earned, take either fun fares on AC (often cheaper than tango fares!), or go on a UA or US ticket, on their planes.
In terms of domestic flights, I agree with the above pieces of advice. I suspect what you are asking is how to get the cheapest fare, with the maximum number of status miles, without paying a penny out of pocket. As mentioned above, look on the ac.com site, and pick the flights that have sold out tango fares. If you are booked a flight with tango fares available, then you will have to pay the difference between tango and fun fares. However, fun fares domestically will only get you half status miles. In terms of overseas flights, they still earn full status miles - sometimes a web fare that you can find from your own research might beat the cheapest fare your travel agent might get you - maybe with the savings to the company, that amount can be covered by the company in upgrading from the domestic tango to domestic fun fares.
In terms of overseas flights, if your company allows business class travel, but it must be discounted business class, do not fly AC - you will only get 1 status mile per mile flown. With the other Star Alliance carriers, you will get 1.25 status mile per mile flown. To go to LHR, if you do not mind a detour, and if the fare is not different from that offered by AC on the direct route to LHR, then take LH or OS via their hubs, or if BMI offers the service in summer, take the YYZ to Manchester route, and then on to LHR.
If you are not uneasy about going via USA to LHR, and if you must go in economy/coach - fares via USA on UA or US may be cheaper than on direct AC flights to LHR - and you would get full status miles.
To maximize the domestic miles that you earn, you need to buy the more expensive freedom or latitude fares, or upgrade from these or the cheaper fun fares. You can not upgrade from tango fares.