...don't.
Everyone feels the need to fix problems. Especially me, since I'm naturally love solving problems and am quite direct. However, few people actually want advice when they talk about their problems. More often than not they just want someone to listen.
The best way to do this is hold eye-contact and paraphrase back what someone has told you. Make 'mmhm' sounds on occasion (but not too frequently). Try cocking your head to the side as well (lead the body and the mind will follow).
There have been too many times when someone has even asked me for advice only to hear me say it and still feel indecisive and need further validation. STFU and go try it or don't ask me for advice. This annoys me to death.
The best method here is inception. Or, as some may call it, the Socratic method.
Whenever someone asks for your advice, just pose the question back to them. Dig deeper by turning whatever advice you'd originally give into the form of a question. For example, if you would tell someone, "try waiting a few days and then go call them and talk about it then," instead say, "What if you waited a few days and then called them?"
Asking someone a question fires up the brain and forces them to think more critically. Most of the time we want to answer our own questions. And, we usually have the best answer anyone could give. It just requires a little push to dig in different directions.