the unmanaged switch may be running a flavor of STP or not.
If the unmanaged switch runs a form of STP it will take part in STP. Being unmanaged it will have default settings like Bridge priority 32768. It is likely that it will run 802.1D that is a single STP instance for all Vlans so interaction with Cisco switches will happen only in Vlan 1.
To avoid that the unmanaged switch becomes the root bridge or the secondary root bridge you have to configure manually the root bridge and the secondary root bridge so that they will have lower then default priorities.
On user ports where you don't expect a switch to be connected you can deploy bpduguard so that the port is put in errordisable when an STP BPDU is detected. This allows to prevent use of unmanaged switches plugged in by end users.
For unmanaged switches not running any form of STP STP bpduguard can detect when two ports from your network devices are connected to it by recieving each other STP BPDUs so do not use bpdu filter on end user ports.
Hope to help
In addition to Giuseppe's great answer, let me add a few points.
Assuming that the unmanaged switch does not run STP at all, some precautions should be taken:
Having managed and unmanaged switches in a network is therefore not recommended, even though I understand that in many cases, it is not easy to perform such a costly upgrade. The network will work in this mixed mode but it is not protected as well as it could be if all switches supported some STP version.