I’m currently maintaining a dedicated web server(Ubuntu 14) running NGINX, MYSQL and a wildcard SSL for the main domain., running OpenSSL 1.0.1f 6 Jan 2014.

What would be the best way to install TLS 1.1, TLS 1.2 ?

The Encryption that the server already supports, thought SSLv1, SSLV2, SSL3 are deprecated.

nmap –script +ssl-enum-ciphers example.com

ssl-enum-ciphers: 
|   SSLv3: 
|     ciphers: 
|       TLS_DHE_RSA_WITH_3DES_EDE_CBC_SHA - strong
|       TLS_DHE_RSA_WITH_AES_128_CBC_SHA - strong
|       TLS_DHE_RSA_WITH_AES_256_CBC_SHA - strong
|       TLS_DHE_RSA_WITH_CAMELLIA_128_CBC_SHA - strong
|       TLS_DHE_RSA_WITH_CAMELLIA_256_CBC_SHA - strong
|       TLS_ECDHE_RSA_WITH_3DES_EDE_CBC_SHA - strong
|       TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA - strong
|       TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA - strong
|       TLS_RSA_WITH_3DES_EDE_CBC_SHA - strong
|       TLS_RSA_WITH_AES_128_CBC_SHA - strong
|       TLS_RSA_WITH_AES_256_CBC_SHA - strong
|       TLS_RSA_WITH_CAMELLIA_128_CBC_SHA - strong
|       TLS_RSA_WITH_CAMELLIA_256_CBC_SHA - strong
|     compressors: 
|       NULL
|   TLSv1.0: 
|     ciphers: 
|       TLS_DHE_RSA_WITH_3DES_EDE_CBC_SHA - strong
|       TLS_DHE_RSA_WITH_AES_128_CBC_SHA - strong
|       TLS_DHE_RSA_WITH_AES_256_CBC_SHA - strong
|       TLS_DHE_RSA_WITH_CAMELLIA_128_CBC_SHA - strong
|       TLS_DHE_RSA_WITH_CAMELLIA_256_CBC_SHA - strong
|       TLS_ECDHE_RSA_WITH_3DES_EDE_CBC_SHA - strong
|       TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA - strong
|       TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA - strong
|       TLS_RSA_WITH_3DES_EDE_CBC_SHA - strong
|       TLS_RSA_WITH_AES_128_CBC_SHA - strong
|       TLS_RSA_WITH_AES_256_CBC_SHA - strong
|       TLS_RSA_WITH_CAMELLIA_128_CBC_SHA - strong
|       TLS_RSA_WITH_CAMELLIA_256_CBC_SHA - strong
|     compressors: 
|       NULL
|_  least strength: strong

NGINX CONFIGURATION FILE

ssl_protocols TLSv1 TLSv1.1 TLSv1.2;
ssl_ciphers "EECDH+ECDSA+AESGCM EECDH+aRSA+AESGCM EECDH+ECDSA+SHA384 EE$4 EECDH EDH+aRSA RC4 !aNULL !eNULL !LOW !3DES !MD5 !EXP !PSK !SRP !DSS";
ssl_prefer_server_ciphers on;

OPENSSL VERSION

OpenSSL 1.0.1f 6 Jan 2014
built on: Mon May  2 16:53:18 UTC 2016
platform: debian-amd64
options:  bn(64,64) rc4(16x,int) des(idx,cisc,16,int) blowfish(idx) 
compiler: cc -fPIC -DOPENSSL_PIC -DOPENSSL_THREADS -D_REENTRANT -DDSO_DLFCN -DHAVE_DLFCN_H -m64 -DL_ENDIAN -DTERMIO -g -O2 -fstack-protector --param=ssp-buffer-size=4 -Wformat -Werror=format-security -D_FORTIFY_SOURCE=2 -Wl,-Bsymbolic-functions -Wl,-z,relro -Wa,--noexecstack -Wall -DMD32_REG_T=int -DOPENSSL_IA32_SSE2 -DOPENSSL_BN_ASM_MONT -DOPENSSL_BN_ASM_MONT5 -DOPENSSL_BN_ASM_GF2m -DSHA1_ASM -DSHA256_ASM -DSHA512_ASM -DMD5_ASM -DAES_ASM -DVPAES_ASM -DBSAES_ASM -DWHIRLPOOL_ASM -DGHASH_ASM
OPENSSLDIR: "/usr/lib/ssl"