I challenge the notion that sales on consecutive days are independent of one another. The comment about diagnostic plots make me think, however, that you have some evidence that they are independent, so let's proceed with that assumption.
First, ANOVA is a linear model. For $k$ groups, your model is:
$$y_i = \beta_0 + \beta_1 I_1 + \beta_2I_2 + \cdots +\beta_{k-1}I_{k-1} +\epsilon_i$$
The $I$ terms are indicator variables (0 or 1) denoting if observation $i$ belongs to group 1, 2, etc. In your case, you have 3 groups (weekday, weekend, holiday), so you have two indicator variables. The third one gets sucked into the intercept term. This has to do with keeping the model matrix of full rank, a technical point that I think is best deferred to a separate question (one that must be addressed somewhere on Cross Validated).
Yale has a decent description of the details of this, as do other posts on Cross Validated.
So far, you probably get what going on and can develop a model matrix to stick in some software to get you the regression equation and some inferences on the parameters to check if the parameter corresponding to the weekend is significant. (R has the lm function.) What might be worth considering is including the particular salesperson. After all, one person may just be better at making sales. Another member may come along and disagree with me on this, but I think that the person should be something called a random effect, which involves somewhat different ways of estimating the parameters and doing inference on them. R has the lme4 package to do random effects through the lmer function.
The gist of a random effect is that the levels are drawn from a larger population. Your three salespeople are the three that you happen to have out of the 7 billion people on Earth, and I suspect that you want your results to generalize, not to be specific to these three salespeople.
The way that I would write this for lmer is L <- lmer(y~I1+I2 +(Katya || Dino || Dave),Sales_Data).
Sales_Data would be a data frame with the headers “I1” (weekend), “I2” (holiday), "Katya", "Dino", and "Dave". All three are indicator variables.
(I concede that I haven't done this in years, and I am torn on whether all three salespeople should be included, or if there should be two with the third being sucked into the intercept term. If someone wants to put their take in a comment...)
This random effects business most likely is new to you, so I don't want to have it get in the way of you doing a decent analysis. ("Perfect is the enemy of good" or something.) If you believe that there is no time dependence, then ANOVA and linear models are both acceptable and, in fact, are equivalent.
We can discuss in the comments (perhaps eventually chat) if you want to pursue the random effects avenue.
