Here is a few ways to play as an assault.
Be a pain in the enemy's ass by rushing them. You want to use a high-power rifle, i would prefer the AEK-971 or XM8, as they are pretty decent and are unlocked early. The grenade launcher is most commonly used, so I recommend using the Grenade upgrade and the Explosive damage upgrade specs, as this can easily soften up enemy resistance from afar, and makes it easier to get kills if you happen to be on the blackhawk without a minigun.
If you are camping outdoors, or going to engage enemies at longer ranges, use the M416 or AUG, as they have low recoil, and good damage. I recommend any optic as the spec, or the ammo spec. I also recommend the grenade launcher as the gadget, useful for engaging larger numbers of enemies. I would use the ceramic body armor spec, as this will allow you to take more damage before dying, letting you hold out longer, or the . Using these specs, you should be able to hold out for a while. If you are going to be engaging enemies in CQC, i would recommend using the Saiga or USAS shotgun, with extended shotgun mag spec, and the Explosives pouch spec. This will let you take out large numbers of enemies, and if you are about to be killed, you will have enough C4 to detonate the whole building, if you had planted it, killing yourself and multiple attackers. The C4 can also be used on enemy vehicles that pass close enough to your spot.
If you are counter-sniping (trying to kill snipers), i recommend using the M16A2 or AN-94. They both have low recoil, high power, and fire fast. With the smoke launcher, you can cover yourself a little better from a sniper that has spotted you, or even shoot it at the sniper to blind him. I would use the 4x scope spec, as this will allow greater zoom, something that helps people countersnipe. The spec 2 perk should have marksman training or magnum ammo (Note: I only recommend magnum ammo as this will help people countersnipe more easily, as well as bringing the power closer to that of a sniper rifle's.), as this can increase accuracy or damage, respectively, which both will help a player. This will help players effectively fight off snipers using the assault class.