Some trains on key routes will also call at extra stops during the event which runs between Thursday, 2 August and Sunday, 12 August.
Athletes from 52 nations will compete across 12 sports during the event, which is hosted by Glasgow. Diving will take place in Edinburgh and golf at Gleneagles.
With thousands of people from all over Europe expected to watch the championship events, ScotRail Alliance said many services would be busier than usual and urged customers to plan their journey ahead of travelling.
The transport firm will have more staff on hand at key stations to ensure that things run smoothly during the European Championships Glasgow 2018.
Graham Heald, ScotRail Alliance head of customer experience, said: “I’m delighted to see yet another fantastic sporting event come to Scotland. We’ll be doing all we can to get people to the games, with more trains and extra carriages on key routes.
“However, services are still expected to be busier than usual, especially towards Edinburgh with the festivals beginning next week. We ask that customers buy their tickets and plan their journey in advance.”
Extra services include additional trains between Motherwell and Garscadden during the morning of Sunday, 5 August for swimming, gymnastics and rowing at Scotstoun Sports Campus, SSE Hydro and Strathclyde Country Park.
A number of services will make an extra stop at Gleneagles between Thursday, 7 August and Sunday 12 August for customers attending the golf team championships.
There will also be an additional early morning service between Glasgow Queen Street, Gleneagles, and Perth on Sunday, 12 August for customers heading to the final round of the golf.
Transport secretary Michael Matheson said: “It’s great to see Glasgow playing host again to one of the biggest sporting competitions in Europe.
“Our transport system has earned an excellent reputation from past events such as the Commonwealth Games and Ryder Cup, so our operators are experienced in getting spectators to venues on time, but also ensuring commuters, residents and tourists can get around with minimal fuss too.
“We want everyone to have an enjoyable time and are working closely with our transport partners to ensure this happens. Plans include extra capacity, services and staff from ScotRail to help things go smoothly.
“Anyone travelling around the city during the European Championships can play their part by planning journeys in advance using all the available information, such as the ScotRail and ‘Get Ready Glasgow’ social media accounts.
“Given these sporting events coincide with the Edinburgh Festivals we appreciate there may be certain pinch points when the network is very busy. We appreciate the public’s patience and understanding during these extremely busy periods.”
Several services on Sunday, 5 August will also call at Dalmarnock – the nearest station to the Emirates Arena – for the cycling. An extra train will run between Garscadden and Airdrie that day for the cycling.