Common signs of a rat infestation include:

.Droppings: Brown Rat droppings are around 17mm in length, dark coloured, and tapered at one end. Rats tend to use an area as a latrine and so droppings tend to be in one place rather than scattered. 
. Damage to stock and property: With continually growing incisors, rats need to gnaw to stop them growing too long. This results in damage to a variety of materials including soft metals. Food left in packaging also becomes short work to feed on.
.Scratching and squeaking noises: Once inside a property, rats can soon increase in numbers and communication/interaction between the colony can become quite vocal and disturbing.
.Smear marks: Rats usually gain access to food and water sources in some dirty places, including sewers. This means that when moving around a building, the dirt from their bodies smears along walls etc. 
.Live sightings:  Rats like most rodents tend to be nocturnal, however with an ever increase in bird feeders and compost bins in garden areas, food sources become more available during daylight hours. Rats adapt to this and so become more active during the day when the food is available. Left alone, numbers can soon increase and the possibility of them wanting to gain access into nearby properties, especially in the winter months, also increases.
.Burrows and Runs: Brown Rats are opportunistic and will use a variety of harbourage to nest amongst. However, they will still create burrows in the ground if this is the best option for them. Rat burrow entrances are smaller in size to a rabbit burrow but bigger than a field mouse burrow entrance (50p coin size). Rats will often create a burrow close to a food/water source. Runs can often be seen leading to and from these sources back to the burrow.