How is the root bridge elected in STP?
How does STP/RSTP determine which bridge is the root bridge, and how are paths to the root bridge selected?
Is the OP referring to single instance RSTP per 802.1w standard or per-vlan RSTP such as Cisco's extension which can yield multiple root bridges through separate spanning-tree instances?
Not sure how much you know about switching and spanning tree but basically when starting out all switches claim that they are the root. All switches send BPDUs (Bridge Protocol Data Unit) which contain a priority and the BID (Bridge ID).
The BID is 8 bytes long. 6 bytes is used for the MAC address of the bridge. 12 bits is used to indicate the VLAN, this is called extended system ID. 4 bits are used to set the priority. Lower priority means it is preferred compared to a higher. The priority is set in multiples of 4096.
If there is a tie in priority then the lowest MAC address will determine which bridge becomes the root.
To select the path to the root the cost to the root is calculated. As the BPDU travels from the root downstream the cost is increased INBOUND. 802.1D-1998 (legacy STP) had a cost of 19 for a FastEthernet interface. The newer standard 802.1D-2004 defines a cost of 200000 for FastEthernet.
If there is a tie in cost then choose the BPDU that came from the switch with lowest BID. If that is a tie as well (multiple links to same switch) port ID comes into play. The port ID is from the upstream switch as well and consists of a port priority and port ID which identifies the interface. The default port priority is 128.
There is a lot to spanning tree but these are the basic steps.