We have gotten a few questions like this one. While I found one good answer for you, I thought I would take this opportunity answer the question better. There are actually two things to consider and not just one.
When you want to retain the links of an old site you have essentially two tasks: one, to redirect from one site to the other properly; two, replicate your old sites link profile on the new site the best that you can. I will explain.
Redirect:
First you will want to redirect your old site to your new site. It is not uncommon that the site structures do not mesh/align. This is okay. The greatest mistake you can make is to selectively redirect pages/directories from the old site to the new site. It is far better to make a blanket redirect from the old site to the new site. This will preserve the value of the old domain as much as possible.
Here is an example of a blanket redirect:
RewriteCond %{HTTP_HOST} ^oldsite\.com$ [NC,OR]
RewriteCond %{HTTP_HOST} ^www\.oldsite\.com$ [NC]
RewriteRule ^(.*)$ http://www.newsite.com/$1 [R=301,L]
You can also use this simpler example:
Redirect permanent / http://www.newsite.com/
Once this is done, on the new site you will want to make specific redirects.
Here are some examples of a specific page redirect:
Redirect permanent /about/aboutus.html http://www.newsite.com/aboutus/
Redirect permanent /checkout/.* http://www.newsite.com/purchase/
Redirect permanent /fashion/ http://www.newsite.com/clothing/
Redirect permanent /books/edgar-allen-poe.html http://www.newsite.com/books/poe/complete-works.html
Once this is done, prepare for the day that you may want to shutdown your old site. This day always seems to come and it is far better to do the work sooner than to wait.
You will want to examine the incoming links to your old site and determine which ones are of value and which ones are not. Of the valuable links, if you can, see if you can have these links changed. Some may be within your control. Some you may have to contact the site owner or webmaster to have changed. Of these, not all will be changed. Do not worry about this. As well, ignore any low value links.
Once this is done, for each link that could not be changed, find new opportunities to create new links to replace them. I always advising working to create a greater link profile to the new site than exists for the old site. Once this is done, you will be free to delete the old domain should you chose to.