Yes, Satan certainly is active today–and he always has been active, because his goal has always been to block God's work. Whenever God is at work, you can be sure Satan also will be at work, counterattacking and trying to stop whatever God is doing.
The Bible doesn't go into great detail about Satan and how he works; after all, our focus should be on God, not Satan. (If we concentrate mainly on Satan we'll become either overly-fearful or overly-fascinated–and both are wrong.) But the Bible does tell us that the devil has a multitude of demons under his authority, just as God has the angelic hosts under His control to do His will.
Never forget two important truths about Satan (whose name means "Adversary"). First, he is real, and he will do everything he can to draw us away from Christ. Yes, he tempts us to do wrong–but most of all, he tempts us to turn away from God. The Bible says, "Be self-controlled and alert. Your enemy the devil prowls around like a roaring lion looking for someone to devour" (1 Peter 5:8).
Second, Satan is a defeated foe! By His death and resurrection Jesus Christ conquered Satan, and some day God will say, "Depart from me ... into the eternal fire prepared for the devil and his angels" (Matthew 25:41). On whose side are you–Satan's or Christ's? Make sure of your salvation by giving your life to Christ today.