I find that relationships build a lot faster in one-on-one conversations than when in groups and multi-tasking also seems to slow the growth. The gregarious trait from the popularity aspirations is supposed to help, too.
In my first file, and in my daughter's game, we were finding the friendship decay and the career requirements to be too much. In my current game, after creating my sims, I started with the Friend to the World aspiration and focused on completing it quickly just to get the beloved trait. One of the sims was created with that aspiration, and another switched to it once entering live mode. The gregarious trait does seem to help, but both sims are building relations fairly well.
My strategy to make friends was to go to the park and introduce my sims to several others. Then, at home, I invited one or two to hang out at the current lot. Each sim got involved in separate conversations, using friendly interactions (click the "more options" to just get the friendly ones instead of all the suggested ones from different categories) and funny interactions occasionally to keep the discussion interesting. I had the sims chat until the friendship bar was nearly full, and then canceled the discussion and invited over another sim. The guest I'd been chatting with wander off to dance to the stereo or get food, and my sim would then chat with the new guest in another room. I avoided group conversations while building friendship. Once the relationship is built, however, group conversation is good for maintaining the friendship. I was able to complete the Friend to the World aspiration in less than a week, while working in the entertainment track.
Chatting with specific sims on the computer also seems to build friendship fairly quickly and one of my sims made a couple of friends that way.
Jess
