I think when it comes to strategy Sawsbuck is a Pokémon that I have probably put the least amount of thought into. I basically just teach it certain moves and it defeats its opponent with ease. As a result this page isn't going to be too big on the how to train your Sawsbuck (although I will probably throw a bit of that in here). Mostly I'll just talk about what I like to do with my Pokémon and go from there.
First thing's first: I like to find a Deerling with an Adamant Nature. This increases its Attack stat while decreasing its Special Attack stat, a stat I generally ignore with Sawsbuck. I'm pretty picky about this and don't like to go with anything but that. I'll take Jolly as a second option though, which increases its speed while decreasing its Special Attack, but only if I'm having difficulty finding one with an Adamant Nature. Characteristics are something worth considering as well, but I generally just ignore them as I find it more work than needed as a casual player. If you're more hardcore into Pokémon battles than I am––which is like not at all––then you'd probably want to pay attention to it.
Ability isn't something I have worried about too much but it is something to keep in mind as well. Abilities Sawsbuck has include Chlorophyll (increases a Pokémon's speed in sunshine), Sap Sipper (increases Attack if hit by a Grass-type move), and Serene Grace (boosts the likelihood of additional effects occurring), its Hidden Ability. I haven't really worried about this too much, but I would likely go with Serene Grace as it has some cool battle effects. One example of this is if Sawsbuck uses Rock Smash it will always drop the opponents Defense instead of doing it only 50% of the time like normal. It's pretty cool. To get this ability, however, you will either need to enter the Dream World (which I'm not even sure if it still exists) or make use of breeding. In Pokémon Omega Ruby/Alpha Sapphire this Ability is easier to get with the DexNav.
Although I haven't really done much with it something to take advantage of is Super Training. Introduced in Pokémon X/Y it is a useful tool to get those EV's (effort values) into the stats you want. It's way nicer than wild Pokémon battles where the EV placements can be a bit random, although it can be a bit tedious to do. Still, it is definitely something worth considering. This tool also exists in Pokémon Omega Ruby/Alpha Sapphire which is pretty awesome.
Last is the moves I'll teach my Sawsbuck. So far in every single playthrough of Pokémon White I have taught it Cut, Jump Kick, Feint Attack and Horn Leech. Cut I can likely swap out for something else, if it weren't for the fact that it was one of my main team Pokémon and I needed it to cut down things, but I'm not sure what I'd replace it with. What I DO know is it would be a Normal-type move.