Which component(s) defines this speed? Is it the switch core?
Smaller switches have fixed ports, some may have a few modular slots, larger switches commonly use port modules (in groups of 24, 12, 8, ...).
Each port has its supported speeds with copper/twisted pair ports being almost universally downward compatible several grades from 1 Gbit/s to 10 Mbit/s, or 10 Gbit/s also supporting 1 Gbit/s or 100 Mbit/s. Optical ports most often support only a single speed, depending on the SFP module fitted. Additionally, only a subset of optical PHYs can be compatible with each other (e.g. 100BASE-FX and 1000BASE-SX use different wavelengths/colors).
Is it possible to decrease the speed to < xGbits?
Downward-compatible ports negotiate speed automatically to the highest mutually supported speed. Some managed switches support limiting the negotiated speed to e.g. 100 or 10 Mbit/s.
Perhaps by using an adapter?
An adapter actually being able to change the link speed is a bridge, or more commonly a switch.
A specific speed requires a minimum cable grade, e.g. Cat-5e for 1000BASE-T. If the cable is below the required quality the link will be unreliable of even doesn't come up at all.
It's usually possible to force a specific link speed on a NIC or a switch. Due to autonegotiation limitations, this should always be done on both sides.
I guess that it's not possible to increase the speed to > xGbit.
You can certainly increase a link's speed from, say 1 Gbit/s to 10 Gbit/s using a bridge/switch in between. However, the usable bandwidth won't actually grow beyond 1 Gbit/s, so there's nothing gained. If a node requires more bandwidth you need to add more or faster network interfaces.
Of course, you can use the increased uplink speed to aggregate multiple 1 Gbit/s ports - a switch can feed ten 1 Gbit/s downlink ports with only a single 10 Gbit/s uplink without any congestion. This is an extremely common scenario - often the downlink capacity is "oversubscribed" when you provide more downlink bandwidth then the uplink can simultaneously support.