Basically, what you're asking is how to scaffold the assembled contigs. To do this, you need some further information. Note that this isn't simple, and your contigs likely have many problems which makes this difficult.
The obvious one is using more sequence data, either paired-end (short inserts) or mate-pair 2nd gen reads (longer distances), or fosmid/cosmid/BAC ends (typically sequenced using Sanger). I'm using RNAseq for this, which seems an obvious thing to do, but I'm not sure it's very common.
You can use a related genome, and map your contigs to that. This will only be reliable to the extent the genomes are closely related.
You can use gene synteny - certain genes tend to occur in a certain order. Again, this depends on how close the other organisms are.
If you have SNP information, you can create a genetic map from linkage groups, this is often successful in grouping contigs by chromosomes.
If it's important, you can check your scaffolding using PCR by designing primers around the edges of the gap between contigs.
Scaffolding is great, but it doesn't get you a chromosome assignment. If you want to be able to order and orient scaffolds to build a chromosome representation you will need an independent map source. That is, you need markers (SNPs, STSs, genes, etc) that have been mapped to chromosomes using a sequence independent method (linkage mapping, RH mapping, FISH mapping). If you can find the same markers in your scaffolds then you can start ordering and orienting the scaffolds along the chromosomes. Early maps such as this (http://www.ncbi.nlm.nih.gov/pubmed/9149939) were critical to ordering and this (http://www.ncbi.nlm.nih.gov/pubmed/16843097) were critical for ordering and orienting human scaffold data to produce the first chromosome assemblies.
It appears that Hi-C sequencing can be used to efficiently group/arrange contigs on chromosome level: