Most of the literature in quant finance assumes that trading is frictionless and taking place in continuous time. Going from continuous to discrete trading is intuitive and does not really disqualify any quantitative model. However, one would think that including transaction costs in real-life trading can potentially wipe out the profits implied by a model or/and create bad hedges. 

In everyday trading, how do traders take into account transaction costs when using quantitative models for pricing? Surely they have to adjust prices and hedges in a certain way? What are the practical implications?

You should try it out yourself - only way to learn.

I will give you one example:

Trade (backtest) the spread between CAC40 and DJ Eurostoxx 50 using futures mid prices only, and then trade it using the bid-ask spread. You will be quite surprised.

For simplicity trade at the close each day.

Conclusion: can be quite a fatal assumption if you need to trade your theory / idea.

Most of the literature in quant finance assumes that trading is frictionless and taking place in continuous time. Going from continuous to discrete trading is intuitive and does not really disqualify any quantitative model. However, one would think that including transaction costs in real-life trading can potentially wipe out the profits implied by a model or/and create bad hedges. 

In everyday trading, how do traders take into account transaction costs when using quantitative models for pricing? Surely they have to adjust prices and hedges in a certain way? What are the practical implications?

There are many market participants for whom the assumption of frictionless trading is not unreasonable (at least for small size). As long as this holds for at least some participants the derivative securities in the market can be priced consistent with this assumption. 

In everyday trading, how do traders take into account transaction costs? 

They pay them.

@Gamal your answer is not helpful, does not clarify the subject to any extent and is certainly not funny.