Around level 4, you will have gained Swain's full combo. Torment and Decrepify followed by Nevermove and some basic attacks will devastate your enemies. If you are too far for his other two abilities, using Nevermove first can allow you to close the distance.
Swain's basic abilities each have different benefits when leveled and maxed over the others.
Decrepify grants moderate damage and a good slowing effect, on a short cooldown and good range. Ensuring foes stay trapped in the tether with Nevermove or allied disables is key. The downside is that you are either forced to choose between safely using it at max range, thus making it easier to break the tether, or going in closer to more reliably get the full effect. It is also not as useful when being ganked/receiving a friendly gank.
As your main AoE and crowd control ability in one, leveling Nevermove makes it more usable by reducing its cooldown significantly. Alongside the damage increase, Swain's farming/pushing becomes much faster and easier, and the snare is absolutely amazing for countering ganks and assisting during one of your own. However, it is unreliable against enemy champions if one is not able to land it consistently, and if they predict you leveling this first, they can grab early Boots of Speed to counter the ability directly.
By itself, Torment offers nice harassment at a low mana cost. Even at low levels, you can take off 2-3 bars of health at a time using Torment followed by autoattacks against a squishier champion. In combination with Ignite, Swain can provide fatal damage output early on. However the damage dealt by Torment alone is slightly low, while your unleveled abilities will not benefit very much from the damage-amp effect. The best scenario in which you would level this ability first is against a squishy target that is more succeptable to the damage from it and Ignite. The worst case is against targets with high sustain or health.
While laning, try to gauge the strength of your opponents to determine the right balance of aggression with Ravenous Flock. If they're stronger, it might be more beneficial to stay back and farm and counter-aggress.
For utility purposes, Decrepify followed by Nevermove makes for a nearly guaranteed root. The time taken to cast Torment can cost you your disables, so choose based on the situation.
Ravenous Flock is not channeled, and cannot be stopped by stuns, silences, or any form of crowd control. You can use it during teamfights to drain the enemies' health, as well as restore health on minions after the fight. With extra spellvamp and a Spirit Visage, one can nearly be an unstoppable force.
You should still be wary of disables preventing you from stopping the spell, especially if left on for longer durations; those few seconds more can quickly deplete your mana pool.
Be cautious when using Ravenous Flock to farm, as it opens you up to ganks, as you will have no survivability.
While escaping, you can activate Ravenous Flock, as it will heal you as your enemies pursue you. This can be very effective because the projectiles prioritizes champions and heals youself 75-88% of the damage dealt to them. Healing with your ultimate while throwing down your slow and snare gives Swain an easy escape.
The best combo for Swain is Torment, Ravenous Flock,Nevermove,Decrepify. This combo is especially effective against melee champions near creeps, because you gain health from the creeps while you engage the enemy champion. This drains your mana quickly however, so make sure to buy some mana items to fuel your combo.
If Swain is doing well, giving him Crest of the Ancient Golem can greatly increase his effectiveness, and even if he is doing poorly, the buff could allow him to make a comeback or at least get back on level ground with his team and the opposition.
With all the control and healing you have as Swain, MR is inherently more important and useful. This is because almost all physical damage is done over time, which your healing counters, and most of the significant physical damage is put off by squishy carries, who are almost free food to your combo.
If you activated Ravenous Flock when engaging an enemy remember to stop the spell if the enemy champion escapes out of your range, if not you could not have enough mana left to use your spells when you reach him resulting in a counterattack, being ganked, or allowing the enemy to escape.
A good harass method is launching Torment inmediately after casting Nevermove, then approach and launch Decrepify and some autoattacks before retreating, this combo should deal around 40%-60% of a squishy enemy champ's health leaving him vulnerable to a final combo of your abilities.
Throwing Torment and Ignite on a dying-yet-retreating enemy will almost always ensure their death, even if they are healed by a moderate amount.
It is also extremely effective to throw this combo on a squishy carry like Caitlyn at the start of a team fight. The damage from this and Swain's other abilities is usually enough to put them into a retreat, cutting away their dps, and may even kill them.
If you aren't satisfied with the one-hit-wonder characteristic of the DFG, a great alternative is Morello's Evil Tome, as it provides greater amounts of the same stats without the restrictive active effect.
Despite his basic abilities outranging the aura of Abyssal Scepter, Swain's high self-healing factor can let him afford to wade closer to the centre of a fight and also indirectly increases his healing as well. It is also a valuable source of magic resistance.
On top of this, if you notice him with a build similar to the second one listed above, you may have no choice but to try to take down the rest of his team before him, as killing him could be extremely time consuming and difficult.