The whole of Israel had to be involved in the selection of its king, and this passage, along with others, may be a reminder that all the people of God have to be involved in the selection of its leaders, a practice which is seen in some denominations in the way their office bearers are chosen.
It is not entirely clear what procedure was used by Samuel here. God had given to the priests of Israel the Urim and Thummim as means of discovering his will (Exod. 28:30), and in 1 Samuel 23:9 David makes use of the priest’s ephod to discover God’s will. Lots were used for identifying offenders (see Achan in Joshua 7:14-18 and Jonathan in 1 Samuel 14:38-42), and were also used by the apostles when they were choosing a replacement for Judas (Acts 1:26).
Should we use such methods today to discover God’s will? There are certain situations in which they should not be used, such as (a) if there is a clear biblical command concerning the situation, (b) if there is a clear biblical principle that can be used in the situation, (c) if such practices are becoming substitutes for taking note of biblical teaching, providential circumstances and wise counsel.
I think it is also the case that there is a difference in asking for a sign as initial direction and asking for one as confirmation of an action that seems to be right, which is what Abraham’s servant did when he met Rebekah (Gen. 24).
The silence of the New Testament letters concerning such practices would suggest they are incompatible with the presence of the Holy Spirit in the church since Pentecost. I suspect that the only type of occasion that such things should be used would be in a situation of danger in which an immediate decision had to be made. Otherwise we should wait on the Lord’s dealing in providence.