How to verify a linear model? Given a dataset and liner model, how can I verify its sufficient quality?
> summary(ll)

Call:
lm(formula = dataset$speedup ~ dataset$cores + I(dataset$cores^2))

Residuals:
    Min      1Q  Median      3Q     Max 
-2.2220 -0.3854 -0.0917  0.3252  7.1028 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)        -0.669882   0.126153   -5.31 1.68e-07 ***
dataset$cores       1.201956   0.011876  101.20  < 2e-16 ***
I(dataset$cores^2) -0.012727   0.000235  -54.16  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8832 on 477 degrees of freedom
Multiple R-squared:  0.9889,    Adjusted R-squared:  0.9888 
F-statistic: 2.122e+04 on 2 and 477 DF,  p-value: < 2.2e-16

Can I conclude, that model fits well since Multiple R-squared = 0.9889?
Alternatively, having the residuals printed, can I conclude, that they are random enough, hence the model fits well?

Can I test is somehow? Or is the intuition sufficient?
 A: From the output, I can say that your model provides an excellent fit to the data (it sounds like you are dealing with simulated data). Moreover, the pvalue related to the F-statistic confirms that your model is extremely better than the one with a constant term only (In my opionion this pvalue is not that useful). You might check also the residuals against the covariates and see if you spot any pattern (see plot(ll)). If not, then the model may be ok.
Of course, you can do a lot of other things. For instance, you might also consider a GAM (Generalized Additive Model) and check if the quadratic form (the one you are using) is better than a GAM. This book, http://www-bcf.usc.edu/~gareth/ISL/getbook.html (you can get a free pdf copy for the site) might be helpful. Hope this helps. 
A: I think your approach is correct and your model explains the data well, without too much bias (so it should generalize well for predictions).
The $R^2$ measure alone tells you how well the model explains all the variability of the data around the mean. Yours does.
Looking at residual plot tells you if your coefficient estimates are biased (something the $R^2$ does not tell you). Yours are not.
By googling I just stumbled upon this blog post which has some nice further explanations about these topics.
