In more formal contexts, one can perform an internet/online search/query without ever mentioning Google:
We performed an online search to identify relevant conference proceedings, journal articles, reports, and academic theses. — Andreas Freitag, Applying Business Capabilities in a Corporate Buyer M&A Process, 2014.
The Rugge Group performed an online search of the trade press to identify leading software developers and to find articles on the cost of developing software. — Ronald G. Albright, Electronic Communications for the Home and Office, 2018.
You have now performed an online query for “web design company” and now the results page is sitting there just waiting for your instructions. — Denver Online Pro, 28.10.2017.
In an attempt to locate the employer, a WHD investigator performed an internet search and located a business going by a similar name and listed as a farm instead of being listed as a trucking company as the complaint indicated. — Gregory D. Kutz, Department of Labor: Case Studies…, 2009.
In a more conversational tone, where performed would seem out of place, one can simply do the search:
Maybe you experienced some of these feelings the last time you did an online search. You had a question, launched an Internet search, roamed around the search results, checked out some of the more relevant items, and hopefully got what you needed. — Patricia A. McLagan, Unstoppable You, 2017.
“I did a search online and found a couple of sites that are really good. One of them was exactly what I was looking for, it was all about the topic I was working on, another site had a load of quotations from other people that were really useful. — James Carmichael, Challenges in Counselling: Research, 2013.
As a sidenote, the German verb googeln (ich google, du googelst, er googelt, ppart. gegoogelt) first made its way into a dictionary in 2004 and is required vocabulary for the B1 certificate in German as a foreign language from the Goethe Institute.