Clade is a branch (at any level) of a phylogenetic tree. The term "lineage" is used variously: either as a synonym of "clade", or for a series of descendants of particular ancestor up to a specific terminal taxon (without side-branchings), or in some less precisely defined meaning.

A clade contains an ancestral organism and all of its descendants, and is thus defined by a node in a phylogenetic tree. The term 'lineage' is more labile and usually defined as a series of ancestral forms leading to a taxon of interest and is therefore more well-defined as a branch (ideally, an edge between the ancestral node and descendant, but in practice/unofficially this often is used to encompass all of the short-branching taxa between the two, so it is a grade).

As for the second question:  The phylogenetic tree (or phylogeny) is the determination.  It is the visual representation of an attempt to reconstruct the history of lineages in relation to each other, based on their current traits and/or genotypes.  There are many methods for doing this, as you may be aware.  The problem is we cannot ever know if we are right.  But, we can increase our confidence in our result in a few ways.  We can use statistical bootstrapping or Bayesian posteriors.  We can use methods that have been shown to work well on simulated or even real (viral) datasets, where the correct answer is known.  These methods can include different types of analyses or different ways of sampling (i.e. number of taxa, outgroup distance, amount of data, type of data). We also tend to feel more confident in trees that are "robust", that is that are found by multiple methods, further increase our confidence.  

Each branch in the tree defines a lineage or clade.  In cladistics, they can also be defined by shared, derived characters, or synapomorphies.  But, for phylogenetic analyses of DNA sequence data using statistical methods (i.e. maximum likelihood or Bayesian), these may be difficult to identify.  

In a phylogeny, a clade represents a monophyletic group, where as a lineage could be an any branch.