You can dance in "Sims 3" alone or with a partner. Your sim will learn more difficult dances as his dance skill bar increases as he practices. A slow dance can only be done with a partner who is slightly romantically interested in your sim. Your sim must have some dancing skill already to have the option of slow dancing.
Load "Sims 3" and start playing your character. Purchase a radio or other audio device to play music.
Practice dancing by yourself with just music playing. You will slowly become better at dancing, which you will notice when your sim does more technical dance manoeuvres.
Invite another sim over to your house, preferably one who your sim is romantically involved with or has feelings for. Prepare a quiet, romantic evening alone if your sim is already married.
Interact with your partner sim to set the mood. You may have to be patient in getting the other sim open enough to dance with you. Sims with shy personality traits will take longer to warm up to the idea of dancing. One of the Sims will eventually suggest a slow dance.
Right click on the other sim to bring up interaction options. Look for the "Dance Together" option. Click it and select "Slow Dance" from the dance choices.