Sometimes, the party may need to split up in order to tackle multiple challenges at once. Since the dynamics of a well-balanced party rely on each member being present in order to cover all skills and abilities, splitting the party almost always results in each group being unprepared for the challenges they face. As such, the party should only split up when absolutely necessary to accomplish their goals.
When the party is split, the GM is effectively officiating multiple separate groups at once. There can be as many groups as there are players, and each group can be in completely different areas of the game world and in different game phases. This is another reason to avoid splitting up the party - not only is it dangerous to your characters, but it can be daunting for your the GM to manage.
While the party is split, the GM alternates focus between each group. In order to keep each group of players involved in the game, the GM should avoid spending too much time on one group. As long as the groups are each in the same game phase, the best approach is to complete one round with a group before moving on to the next group.
If the groups are in different game phases, then time differences must be taken into account. In order to enable inter-group communication and avoid metagaming, it's crucial that the in-game time be kept synchronized across all groups of a split party. This may require the GM to spend an extended period of time with one group. For example, if one half of a split party completes three rounds of adventuring while the other half completes three rounds of combat, then significantly more time will have elapsed for the first group than for the second, and there is now a time disconect between the two groups, which leads to confusion when the party reconvenes. As such, it's best for the GM to finish combat with one group before moving on to another.
Just because the party members are not all in the same physical location, does not mean the party is split. If the party is working synchronously together on the same objective from different locations, then the game can still be played as a single group. For example, if one person breaks off from the group mid-fight to cross through a secret passage and ambush the enemy, or if the group splits up while remaining in direct communication via walkie-talkies, the party can remain as one group.